Updated on 2025/10/19

写真a

 
YANAGAWA,Kohji
 
Organization
Faculty of Engineering Science Professor
Title
Professor
Contact information
メールアドレス
External link

Degree

  • Doctor of Science ( 1996.3 )

Research Interests

  • combinatorics

  • commutative algebra

Research Areas

  • Natural Science / Algebra

Education

  • Nagoya University   Graduate School, Division of Natural Science

    - 1996

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  • Nagoya University   Faculty of Science

    - 1991

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    Country: Japan

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  • Nagoya University   Graduate School, Division of Natural Science

    1996

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    Country: Japan

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Research History

  • 1996-1997 Niigata University, Research Assistant 1997-2007 Osaka University, Research Assistant2007- Kansai University Associate Professor

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  • 1996-1997 Niigata University, Research Assistant1997-2007 Osaka University, Research Assistant2007- Kansai University Associate Professor

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Professional Memberships

Papers

  • Arithmetic on $q$-deformed rational numbers Reviewed

    Takeyoshi Kogiso, Kengo Miyamoto, Xin Ren, Michihisa Wakui, Kohji Yanagawa

    Arnold Mathematical Journal   011 ( 003 )   42 - 92   2025.10

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Association for Mathematical Research  

    DOI: 10.56994/armj.011.003.003

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  • Elementary construction of the minimal free resolution of the Specht ideal of shape (n − d,d) Reviewed

    Kosuke Shibata, Kohji Yanagawa

    Journal of Algebra   Vol 634, no. 15, pp. 563-584   563 - 584   2023.11

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    Publishing type:Research paper (scientific journal)   Publisher:Elsevier BV  

    DOI: 10.1016/j.jalgebra.2023.07.028

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  • Gröbner Bases of Radical Li–Li Type Ideals Associated with Partitions Reviewed

    Xin Ren, Kohji Yanagawa

    SIAM Journal on Discrete Mathematics   Vol. 37, No. 4, ( 4 )   2382 - 2396   2023.10

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    Publishing type:Research paper (scientific journal)   Publisher:Society for Industrial & Applied Mathematics (SIAM)  

    DOI: 10.1137/23M1547627

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  • Elementary construction of minimal free resolutions of the Specht ideals of shapes (n−2,2) and (d,d,1) Reviewed

    Shibata, Kosuke, Yanagawa, Kohji

    Journal of Algebra and Its Applications   Vol. 22, No. 9 2350199   2023.9

  • A note on the reducedness and Grobner bases of Specht ideals Reviewed

    Satoshi Murai, Hidefumi Ohsugi, Kohji Yanagawa

    COMMUNICATIONS IN ALGEBRA   Vol. 50,pp. 5430-5434 ( 12 )   5430 - 5434   2022.12

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1080/00927872.2022.2085288

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  • Graded Cohen–Macaulay Domains and Lattice Polytopes with Short h-Vector Reviewed

    Katthän, Lukas, Yanagawa, Kohji

    Discrete & Computational Geometry   Volume 68, issue 2, pp. 608–617   2022.9

  • Regularity of Cohen-Macaulay Specht ideals Reviewed

    SHIBATA, Kosuke, YANAGAWA, Kohji

    Journal of Algebra   Vol. 582, Pages 73-87   73 - 87   2021.9

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    Publishing type:Research paper (scientific journal)   Publisher:Elsevier BV  

    DOI: 10.1016/j.jalgebra.2021.04.022

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  • When is a Specht ideal Cohen–Macaulay? Reviewed

    YANAGAWA,Kohji

    Journal of Commutative Algebra   Volume 13 , No. 4, 589–608   2021

  • Alexander duality for the alternative polarizations of strongly stable ideals Reviewed

    SHIBATA, Kosuke, YANAGAWA,Kohji

    Communications in Algebra   Vol. 48, pp. 3011-3030   2020.7

  • Vandermonde determinantal ideals Reviewed

    WATANABE, Junzo, YANAGAWA, Kohji

    Mathematica Scandinavica   Vol 125, No 2, pp.179-184   2019.10

  • LYUBEZNIK NUMBERS OF LOCAL RINGS AND LINEAR STRANDS OF GRADED IDEALS Reviewed

    ÀLVAREZ MONTANER, Josep, YANAGAWA,Kohji

    Nagoya Mathematical Journal   Volume 231,pp. 23-54   2018.9

  • The Cohen–Macaulayness of the bounded complex of an affine oriented matroid Reviewed

    Ryota Okazaki, Kohji Yanagawa

    Journal of Combinatorial Theory. Series A   157   1 - 27   2018.7

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Academic Press Inc.  

    DOI: 10.1016/j.jcta.2018.01.004

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  • Non-level semi-standard graded Cohen-Macaulay domain with h-vector (h(0), h(1), h(2)) Reviewed

    Akihiro Higashitani, Kohji Yanagawa

    JOURNAL OF PURE AND APPLIED ALGEBRA   222 ( 1 )   191 - 201   2018.1

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.jpaa.2017.03.011

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  • A canonical module characterization of Serre's (R-1) Reviewed

    Lukas Katthaen, Kohji Yanagawa

    COMMUNICATIONS IN ALGEBRA   45 ( 2 )   600 - 605   2017

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1080/00927872.2016.1172611

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  • Properties of Lyubeznik numbers under localization and polarization Reviewed

    Arindam Banerjee, Luis Nunez-Betancourt, Kohji Yanagawa

    JOURNAL OF PURE AND APPLIED ALGEBRA   219 ( 11 )   4872 - 4888   2015.11

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.jpaa.2015.03.010

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  • Dualizing complexes of seminormal affine semigroup rings and toric face rings Reviewed

    Kohji Yanagawa

    JOURNAL OF ALGEBRA   425   367 - 391   2015.3

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.jalgebra.2014.11.013

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  • On CW complexes supporting Eliahou-Kervaire type resolutions of Borel fixed ideals Reviewed

    Ryota Okazaki, Kohji Yanagawa

    COLLECTANEA MATHEMATICA   66 ( 1 )   125 - 147   2015.1

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/s13348-014-0104-0

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  • Squarefree P-modules and the cd-index Reviewed

    Satoshi Murai, Kohji Yanagawa

    ADVANCES IN MATHEMATICS   265   241 - 279   2014.11

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.aim.2014.07.037

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  • Addendum to "Frobenius and Cartier algebras of Stanley-Reisner rings" [J. Algebra 358 (2012) 162-177] Reviewed

    Josep Àlvarez Montaner, Kohji Yanagawa

    Journal of Algebra   414   300 - 304   2014.9

  • Alternative polarizations of Borel fixed ideals, Eliahou-Kervaire type resolution and discrete Morse theory Reviewed

    Ryota Okazaki, Kohji Yanagawa

    JOURNAL OF ALGEBRAIC COMBINATORICS   38 ( 2 )   407 - 436   2013.9

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/s10801-012-0409-6

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  • ALTERNATIVE POLARIZATIONS OF BOREL FIXED IDEALS Reviewed

    Kohji Yanagawa

    NAGOYA MATHEMATICAL JOURNAL   207   79 - 93   2012.9

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1017/S0027763000022315

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  • SLIDING FUNCTOR AND POLARIZATION FUNCTOR FOR MULTIGRADED MODULES Reviewed

    Kohji Yanagawa

    COMMUNICATIONS IN ALGEBRA   40 ( 3 )   1151 - 1166   2012

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1080/00927872.2010.547540

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  • HIGHER COHEN-MACAULAY PROPERTY OF SQUAREFREE MODULES AND SIMPLICIAL POSETS Reviewed

    Kohji Yanagawa

    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   139 ( 9 )   3057 - 3066   2011.9

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1090/S0002-9939-2011-10734-2

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  • Dualizing complex of the face ring of a simplicial poset Reviewed

    Kohji Yanagawa

    JOURNAL OF PURE AND APPLIED ALGEBRA   215 ( 9 )   2231 - 2241   2011.9

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.jpaa.2011.02.009

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  • Alexander duality and Stanley depth of multigraded modules Reviewed

    Ryota Okazaki, Kohji Yanagawa

    JOURNAL OF ALGEBRA   340 ( 1 )   35 - 52   2011.8

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.jalgebra.2011.05.028

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  • DUALIZING COMPLEX OF A TORIC FACE RING Reviewed

    Ryota Okazaki, Kohji Yanagawa

    NAGOYA MATHEMATICAL JOURNAL   196   87 - 116   2009.12

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1017/S0027763000009806

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  • LINEARITY DEFECT AND REGULARITY OVER A KOSZUL ALGEBRA Reviewed

    Kohji Yanagawa

    MATHEMATICA SCANDINAVICA   104 ( 2 )   205 - 220   2009

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  • Notes on C-graded modules over an affine semigroup ring K[C] Reviewed

    Kohji Yanagawa

    COMMUNICATIONS IN ALGEBRA   36 ( 8 )   3122 - 3146   2008

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1080/00927870802104295

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  • Linearity defects of face rings Reviewed

    Ryota Okazaki, Kohji Yanagawa

    JOURNAL OF ALGEBRA   314 ( 1 )   362 - 382   2007.8

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.jalgebra.2007.02.049

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  • BGG correspondence and Romer's theorem on an exterior algebra Reviewed

    Kohji Yanagawa

    ALGEBRAS AND REPRESENTATION THEORY   9 ( 6 )   569 - 579   2006.12

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/s10468-006-9037-y

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  • Castelnuovo-Mumford regularity for complexes and weakly Koszul modules Reviewed

    Kohji Yanagawa

    JOURNAL OF PURE AND APPLIED ALGEBRA   207 ( 1 )   77 - 97   2006.9

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.jpaa.2005.09.014

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  • Dualizing complex of the incidence algebra of a finite regular cell complex Reviewed

    YANAGAWA Kohji

    Illinois Journal of Mathematics   Vol.49, no.4, pp.1221--1243.   2005

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    Grant-in-Aid for Encouragement of Young Scientists

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  • Derived category of squarefree modules and local cohomology with monomial ideal support Reviewed

    K Yanagawa

    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN   56 ( 1 )   289 - 308   2004.1

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.2969/jmsj/1191418707

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  • Stanley-Reisner rings, sheaves, and Poincart-Verdier duality Reviewed

    K Yanagawa

    MATHEMATICAL RESEARCH LETTERS   10 ( 5-6 )   635 - 650   2003.9

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.4310/MRL.2003.v10.n5.a7

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  • Local cohomology of Stanley-Reisner rings with supports in general monomial ideals Reviewed

    Reiner, V, Welker, V, K Yanagawa

    JOURNAL OF ALGEBRA   244 ( 2 )   706 - 736   2001.10

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1006/jabr.2001.8932

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  • Bass numbers of local cohomology modules with supports in monomial ideals Reviewed

    K Yanagawa

    MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY   131   45 - 60   2001.7

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1017/S030500410100514X

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  • Sheaves on finite posets and modules over normal semigroup rings Reviewed

    K Yanagawa

    JOURNAL OF PURE AND APPLIED ALGEBRA   161 ( 3 )   341 - 366   2001.7

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/S0022-4049(00)00095-5

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  • Generic and cogeneric monomial ideals Reviewed

    E Miller, B Sturmfels, K Yanagawa

    JOURNAL OF SYMBOLIC COMPUTATION   29 ( 4-5 )   691 - 708   2000.4

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1006/jsco.1999.0290

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  • Alexander duality for Stanley-Reisner rings and squarefree N-n-graded modules Reviewed

    K Yanagawa

    JOURNAL OF ALGEBRA   225 ( 2 )   630 - 645   2000.3

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1006/jabr.1999.8130

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  • F-Delta type free resolutions of monomial ideals Reviewed

    K Yanagawa

    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   127 ( 2 )   377 - 383   1999.2

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1090/S0002-9939-99-04947-3

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  • Squarefree modules and local cohomology modules at monomial ideals Invited Reviewed

    K Yanagawa

    LOCAL COHOMOLOGY AND ITS APPLICATIONS   226   207 - 231   1999

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    Language:English   Publishing type:Research paper (international conference proceedings)  

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  • Associated primes and arithmetic degrees Reviewed

    C Miyazaki, W Vogel, K Yanagawa

    JOURNAL OF ALGEBRA   192 ( 1 )   166 - 182   1997.6

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1006/jabr.1996.6952

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  • On the regularities of arithmetically Buchsbaum curves Reviewed

    Kohji Yanagawa

    Mathematische Zeitschrift   226 ( 1 )   155 - 163   1997

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Springer New York  

    DOI: 10.1007/PL00004331

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  • A characterization of integral curves with Gorenstein hyperplane sections Reviewed

    K Yanagawa

    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   124 ( 5 )   1379 - 1384   1996.5

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1090/S0002-9939-96-03163-2

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  • Castelnuovo's lemma and h-vectors of Cohen-Macaulay homogeneous domains Reviewed

    K Yanagawa

    JOURNAL OF PURE AND APPLIED ALGEBRA   105 ( 1 )   107 - 116   1995.11

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/0022-4049(94)00139-1

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  • SOME GENERALIZATIONS OF CASTELNUOVO LEMMA ON ZERO-DIMENSIONAL SCHEMES Reviewed

    K YANAGAWA

    JOURNAL OF ALGEBRA   170 ( 2 )   429 - 439   1994.12

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1006/jabr.1994.1346

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Presentations

  • Transposes in the q-deformed modular group and their applications to q-deformed rational numbers

    任 鑫, 柳川 浩二

    日本数学会2025年度秋季総合分科会  2025.9 

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    Event date: 2025.9

    Language:Japanese  

    File: 25秋日本数学会(handout).pdf

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  • 単体的ポセットの組合せ論的可換代数 Invited

    柳川 浩二

    第29回代数学若手研究会  2025.3 

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    Event date: 2025.3 - 2025.10

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    File: 若手研究会発表(handout).pdf

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  • Arithmetic and combinatorics on q-deformed rationals Invited

    Commutative Algebra and Projective Algebraic Geometry in Kumamoto, -- on the occasion of Prof. Miyazaki's 65  2024.12 

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    Event date: 2024.12

    Language:English   Presentation type:Oral presentation (invited, special)  

    File: chikashi65(handout).pdf

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  • Local cohomology modules at ideals associated with simplicial posets

    Kohji Yanagawa

    RIMS Workshop "The 45th Japan Symposium on Commutative Algebra"  2024.11 

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    Event date: 2024.11

    Language:English   Presentation type:Oral presentation (general)  

    File: 24RIMS-beamer(handout).pdf

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  • Lyubeznik numbers of Stanley-Reisner ideals, and more... Invited

    柳川浩二

    空間の代数的・幾何的モデルとその周辺  2024.8 

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    Event date: 2024.8

    Presentation type:Oral presentation (invited, special)  

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  • Gr¨obner bases of radical Li–Li type ideals associated with partitions

    MSJ Autumn Meeting 2023  2023.9 

  • Regularity of Cohen-Macaulay Specht ideals

    柴田 孝祐, 柳川 浩二

    第41回可換環論シンポジウム  2019.11 

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    Venue:倉敷シーサイドホテル  

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  • Squarefree 加群とその応用, I, II

    柳川 浩二

    組合せ論と可換代数オータムセミナー  2019.9 

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    Venue:静岡大学  

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  • Specht ideal による剰余環の Cohen-Macaulay 性 Invited

    柳川 浩二

    東京可換環論セミナー  2019.4 

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    Venue:東京大学  

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  • When is a Specht ideal Cohen-Macaulay?

    YANAGAWA,Kohji

    1147th AMS Meeting, Spring Central and Western Joint Sectional Meeting, Special Session on Commutative Algebra and its Environs,  2019.3 

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    Venue:University of Hawaii at Manoa  

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  • Strongly stable ideal の既約分解と局所コホモロジーの関係

    柴田 孝祐, 柳川 浩二

    日本数学会 2019年度年会 代数学分科会  2019.3 

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    Venue:東京工業大学  

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  • Strongly stable ideal のalternative polarization とそのAlexander 双対 について

    柴田 孝祐, 柳川 浩二

    日本数学会 秋季総合分科会 代数学分科会  2018.9 

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    Venue:岡山大学  

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  • Homological methods in combinatorial commutative algebra I, II

    YANAGAWA,Kohji

    The 51st Symposium on Ring Theory and Representation Theory  2018.9 

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    Venue:Okayama University of Science  

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  • Stanley-Reisner 環の理論におけるホモロジカルな手法, I,II

    柳川 浩二

    第8回 (非)可換代数とトポロジー  2018.2 

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    Venue:信州大学  

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  • When is a Specht ideal Cohen-Macaulay?

    YANAGAWA,Kohji

    The 39th Japan Symposium on Commutative Algebra  2017.11 

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    Venue:Research Institute for Mathematical Sciences, Kyoto University  

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  • When is a Specht ideal Cohen-Macaulay?

    YANAGAWA,Kohji

    2017.8 

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  • Non-level semi-standard graded Cohen-Macaulay domains with h-vectors (h_0, h_1, h_2)

    Akihiro Higashitani, Kohji Yanagawa

    The 38th Symposium on Commutative Algebra  2016.11 

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    Venue:International productivity center, Shonan international village  

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  • Non-level semi-standard graded Cohen-Macaulay domains with h-vectors (h_0, h_1, h_2)

    東谷 章弘, 柳川 浩二

    日本数学会 秋季総合分科会 代数学分科会  2016.9 

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    Venue:関西大学  

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  • Lyubeznik numbers of local rings and linear strands of graded ideals

    YANAGAWA,Kohji

    2016.3 

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  • The Cohen-Macaulayness of the bounded complex of an affine oriented matroid

    OKAZAKI, Ryota, YANAGAWA,Kohji

    2015.11 

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  • アフィン有向マトロイドのbounded complex のCohen-Macaulay 性とマトロイド・イデアルのCohen-Macaulay性

    岡崎 亮太, 柳川 浩二

    日本数学会 秋季総合分科会 代数学分科会  2015.9 

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    Venue:京都産業大学  

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  • The Cohen-Macaulayness of the bounded complex of an affine oriented

    YANAGAWA,Kohji

    2015.8 

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  • Serre の(R1) 条件の標準加群による特徴づけ

    柳川 浩二

    第7回岡山可換代数表現セミナー  2015.6 

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    Venue:岡山大学  

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  • Lyubeznik numbers of local rings and linear strands of graded ideals

    Kohji Yanagawa

    The 36th Symposium on Commutative Algebra  2014.11 

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    Venue:International productivity center, Shonan international village  

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  • 単項式イデアルの Lyubeznik 数 ~ polarization と局所化

    柳川 浩二

    2014.11 

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    Venue:岡山大学  

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  • 単項式イデアルの Lyubeznik 数 ~ polarizationと局所化

    柳川 浩二

    第4回岡山可換代数表現セミナー  2014.11 

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    Venue:岡山大学  

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  • 有向マトロイドに付随する単項式イデアル

    柳川 浩二

    組合せ論と可換代数サマーセミナー2014  2014.9 

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    Venue:宮島コーラルホテル  

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  • 多面体的複体の flag f-列について

    村井聡, 柳川浩二

    日本数学会2014年度年会 代数学分科会  2014.3 

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    Venue:学習院大学  

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  • 単項式イデアルの Lyubeznik table

    柳川 浩二

    組合せ論と可換代数サマーセミナー  2013.8 

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    Venue:下関市生涯学習プラザ  

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  • Dualizing complexes of seminormal affine semigroup rings and toric face rings

    Kohji Yanagawa

    The 34th symposium on commutative algebra in Japan  2012.11 

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    Venue:International Productivity Center (Hayama, Kanagawa )  

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  • On a minimal free resolution of a Borel fixed ideal and its supporting CW complex

    Ryota Okazaki, Kohji Yanagawa

    The Mathematical Society of Japan, Autumn Meeting 2012  2012.9 

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    Venue:Kyushu University  

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  • Free resolutions of (variants of) Borel fixed ideals

    Kohji Yanagawa

    The 52nd Algebra Symposium  2012.8 

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    Venue:Research Institute for Mathematical Sciences (Kyoto University)  

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  • Alternative polarizations of Borel fixed ideals, Eliahou-Kervaire type resolution and discrete Morse theory

    Yanagawa, Kohji

    The 7th Japan-Vietnam Joint Seminar on Commutative Algebra  2011.12 

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    Venue:Quy Nhon University (Vietnam)  

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  • Alternative polarizations of Borel fixed ideals and Eliahou-Kervaire type

    Ryota Okazaki, Kohji Yanagawa

    2011.9 

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  • Derived categories and topological methods in combinatorial commutative algebra I, II

    YANAGAWA Kohji

    2011.9 

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    Venue:Research Institute for Mathematical Sciences, Kyoto University  

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  • Sliding functor and polarization functor for multigraded modules

    YANAGAWA Kohji

    The 6th Japan-Vietnam Joint Seminar on Commutative Algebra  2010.12 

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    Venue:International productivity center,Shonan international village  

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  • On the face ring of a simplicial poset

    YANAGAWA Kohji

    The 5-th Japan-Vietnam Joint Seminar on Commutative Algebra  2010.1 

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    Venue:Hanoi Institute of Mathematics  

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  • Recent topics on derived categories in combinatorial commutative algebra

    YANAGAWA Kohji

    Workshop on "Syzygies of Projective Varieties"  2009.9 

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    Venue:Saga University  

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  • Dualizing complex of a toric face ring

    YANAGAWA Kohji

    Pacific Rim Mathematical Association (PRIMA) Congress  2009.6 

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    Venue:The University of New South Wales  

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Works

  • MFO-RIMS Tandem Workshop: Symmetries on Polynomial Ideals and Varieties (hybrid meeting)

    柳川 浩二

    2021.9

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    同研究集会の日本側の副代表を務めた。日本側は完全オンラインであるが、主幹の機関は、オーバーヴォルファッハ数学研究所(ドイツ)と京都大学数理解析研究所。

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Research Projects

  • 組合せ論的可換代数への圏論的アプローチの深化

    Grant number:25K06928  2025.4 - 2029.3

    日本学術振興会  科学研究費助成事業  基盤研究(C)

    柳川 浩二

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    Grant amount:\3770000 ( Direct Cost: \2900000 、 Indirect Cost:\870000 )

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  • The study on ring theoretic properties and Groebner basis of Specht ideals

    Grant number:22K03258  2022.4 - 2025.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

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    Grant amount:\2210000 ( Direct Cost: \1700000 、 Indirect Cost:\510000 )

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  • The Cohen-Macaulay property of ideals associated with subspace arrangements

    Grant number:19K03456  2019.4 - 2022.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

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    Grant amount:\2990000 ( Direct Cost: \2300000 、 Indirect Cost:\690000 )

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  • Application of commutative algebra to topological study on affine oriented matroids

    Grant number:16K05114  2016.4 - 2020.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

    Yanagawa Kohji

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    Grant amount:\3250000 ( Direct Cost: \2500000 、 Indirect Cost:\750000 )

    Just before this project started, the author and his coworker (almost ) showed that if the ideal associated with an affine oriented matroid M is Cohen-Macaulay (CM,for short), then the bounded complex of M is a contractible homology manifold (with boundary). In this situation, we conjectured that the bounded complex is homeomorphic to a closed ball. This conjecture is the main aim of this project. Finally, we proved the conjecture when the dimension is at most 3. We also showed that the bounded complex is a topological manifold in the dimension 4 case.
    In the latter period of this project, the Specht ideals have been a main object of the study.We completely determined the CM Specht ideals in the characteristic 0 case.

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  • Arithmetical rank of Stanley-Reisner ideals and projective dimension of their powers

    Grant number:26400049  2014.4 - 2017.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    Terai Naoki, YOSHIDA KENICHI, YANAGAWA KOUJI, KIMURA KYOUKO

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    Grant amount:\4810000 ( Direct Cost: \3700000 、 Indirect Cost:\1110000 )

    We studied the projective dimension of symbolic powers of squarefree monomial ideals in a polynomial ring. We proved that the projective dimension of the symbolic power of the edge ideal of a very well-covered graph increases with respect to the exponent. Since a well-covered bipartite graph is very well-covered and since the symbolic powers and ordinary powers coincide for the edge ideal of a bipartite graph, it implies that the projective dimension of the ordinary power of the edge ideal of a very well-covered graph increases. Moreover, we showed that the projective dimension of the symbolic power of the edge ideal of a graph with a vertex of degree one increases with respect to the exponent.

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  • Application of New Methods of Combinatorial Topology to Commutative Algebra

    Grant number:25400057  2013.4 - 2016.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

    Yanagawa Kohji

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    Grant amount:\2860000 ( Direct Cost: \2200000 、 Indirect Cost:\660000 )

    With Spanish and American coauthors, I studied the Lyubeznik numbers of the quotient rings of polynomial rings by monomial ideals. For example, we showed that the procedure of "polarization" essentially preserves this invariant. With Prof. S. Murai, I studied the "cd-index" of flag complexes using the notion of squarefree modules. I also studied cellular free resolutions of monomial ideals with Prof. R. Okazaki. We applied this method to the study of affine oriented matroids.

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  • Minimal free resolutions and the arithmetical rank of Stanley-Reisner ideals

    Grant number:23540053  2011 - 2013

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    TERAI Naoki, UEHARA Tsuyoshi, ICHIKAWA Takashi, MIYAZAKI Chikashi, KAWAI Shigeo, YOSHIDA Kenichi, YANAGAWA Kouji, KIMURA Kyouko, MURAI Satoshi

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    Grant amount:\5070000 ( Direct Cost: \3900000 、 Indirect Cost:\1170000 )

    We studied the arithmetical rank of Stanly-Reisner ideals, which are squarefree monomial ideals in a polynomial ring. It is known that the arithmetical rank of a Stanley-Reisner ideal is greater than or equal to the projective dimension of the Stanley-Reisner ring, which is the length of the minimal free resolutions of the quotient ring. As for the edge ideal of a forest, Barile conjectures that these numbers will be coincident. We proved it. As for a Gorenstein Stanly-Reisner ideal of height three, we proved that its arithmetical rank is equal to the projective dimension of the Stanly-Reisner ring, too.

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  • The applications of derived categories and topological methods to combinatorial commutative algebra

    Grant number:22540057  2010 - 2012

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

    YANAGAWA Kohji

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    Grant amount:\2990000 ( Direct Cost: \2300000 、 Indirect Cost:\690000 )

    Developing a result of Nagel and Reiner, the author and R. Okazaki studied the non-standard polarization of a Borel fixed ideal, and gave its minimal free resolution. This resolution is supported by a regular CW complex, which can be “interpreted” by the discrete Morse theory in the framework constructed by Welker et al.
    The author also studied the dualizing complexes of seminormal affine semigroup rings and toric face rings. In this work, the preceding results of Bruns et al and Nguyes are re-formulated and improved using derived categories.

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  • Application of Koszul duality to commutative algebra

    Grant number:19540028  2007 - 2009

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

    YANAGAWA Kouji, TERAI Naoki, WAKUI Michihisa, MORI Izuru, WAKAMATSU Takayoshi

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    Grant amount:\3900000 ( Direct Cost: \3000000 、 Indirect Cost:\900000 )

    The author has been applied the theory of derived categories (e.g., Koszul duality) to the study of combinatorial commutative algebra. The main aim of this research project was to extend this idea and results to general commutative algebra. In this direction, results related to the coherent property of rings were obtained, and the paper was published in an academic journal in 2009. Around 2008, the author slightly changed the direction of the research, and begun to study relatively new objects of combinatorial commutative algebra for which we cannot use usual methods. In this direction, the author has written several papers. Some of them have been published in an academic journal.

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  • THE RING OF DIFFERENTIAL OPERATORS ON AN AFFINE TORIC VARIETYAND ITS APPLICATIONS

    Grant number:18540002  2006 - 2008

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    SAITO Mutsumi, YAMASHITA Hirosh, YANAGAWA Kohji, SHIMADA Ichiro, NUMATA Yasuhide, YANAGAWA Kohji, SHIMADA Ichiro, NUMATA Yasuhide

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    Grant amount:\4060000 ( Direct Cost: \3400000 、 Indirect Cost:\660000 )

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  • Study on minimal free resolution of Stanley-Reisner rings

    Grant number:18540041  2006 - 2007

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    TERAI Naoki, NAKAHARA Tohru, UEHARA Tsuyoshi, ICHIKAWA Takashi, YOSHIDA Ken-ichi, YANAGAWA Kohji

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    Grant amount:\4010000 ( Direct Cost: \3500000 、 Indirect Cost:\510000 )

    The purpose of this research is to study algebraic and combinatorial properties of minimal free resolution of Stanley-Reisner rings. We focused on the relation between the multiplicity and the Castelnuovo-Mumford regularity of Stanley-Reisner rings.
    Before the academic year 2005 we proved that the Castelnuovo-Mumford regularity of a Stanley-Reisner ideal is less than or equal to the dimension d of the Stanley-Reisner rings if its multiplicity is less than or equal to d. Moreover we verified that the Castelnuovo-Mumford regularity of a Stanley-Reisner ideal is less than or equal to d if its multiplicity is less than or equal to 2d-1, and if the degree of generators of the Stanley-Reisner ideal is less than or equal to d
    In the academic year 2006, developing these results, we proved that the Castelnuovo-Mumford regularity of a Stanley-Reisner ideal is less than or equal to d if its multiplicity is less than or equal to 3d-2, and if the degree of generators of the first syzygy module of the Stanley-Reisner ideal is less than or equal to d+1. From this result we conjectured that the Castelnuovo-Mumford regularity of a Stanley-Reisner ideal is less than or equal to d if its multiplicity is less than or equal to (p+2)d- (p-1), and if the degree of generators of the p-th syzygy module of the Stanley-Reisner ideal is less than or equal to d+p. In the academic year 2007 we proved that the above conjecture holds if the dimension of the Stanley-Reisner rings is 2 or 3. We also found that this conjecture is a generalization of the lower bound theorem, that is famous in convex polytope theory, in the facet case.

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  • Study on minimal free resolution of Stanley-Reisner rings

    Grant number:16540028  2004 - 2005

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    TERAI Naoki, TANAKA Tatsuji, NAKAHARA Tohru, ICHIKAWA Takashi, YOSHIDA Ken-ichi, YANAGAWA Kohji

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    Grant amount:\3600000 ( Direct Cost: \3600000 )

    The purpose of this research is to study algebraic and combinatorial properties of minimal free resolution of Stanley-Reisner rings and to consider its combinatorial applications.
    In the academic year 2004 we studied Buchsbaum Stanley-Reisner rings with linear resolution. We determined the lower bound for the multiplicity of Stanley-Reisner rings. And we showed that they have linear resolution if they possess the minimal multiplicity. We also showed a necessary and sufficient condition for Buchsbaum Stanley-Reisner rings to have linear resolution in terms of the reduced homology groups of the corresponding simplicial complex and its links.
    In the academic year 2005 we mainly studied the relation between the multiplicity of Stanley-Reisner rings and their Castelnuovo-Mumford regularity. We proved that the Castelnuovo-Mumford regularity of a Stanley-Reisner ideal is less than or equal to the dimension d if its multiplicity is less than or equal to d. Moreover we verified that the Castelnuovo-Mumford regularity of a Stanley-Reisner ideal is less than or equal to d if its multiplicity is less than or equal to 2d-1, and if the degree of generators of the Stanley-Reisner ideal is less than or equal to d
    We also investigated Stanley-Reisner rings with d-linear resolution among those with linear resolution intensively. Using the above result we showed that a Stanley-Reisner ring has d-linear resolution if its multiplicity is less than or equal to d and if the degree of generators of the Stanley-Reisner ideal is more than or equal to d. Moreover we showed that a Stanley-Reisner ring has d-linear resolution if its multiplicity is less than or equal to 2d-1 and if the degree of generators of the Stanley-Reisner ideal is d. By Alexander duality, we also verified that a Stanley-Reisner ring is Cohen-Macaulay if its multiplicity is large enough.

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  • 層や導来圏の理論を用いた組合せ論的可換代数の研究

    Grant number:15740014  2003 - 2005

    日本学術振興会  科学研究費助成事業 若手研究(B)  若手研究(B)

    柳川 浩二

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    Grant amount:\3400000 ( Direct Cost: \3400000 )

    昨年度に執筆した論文"Dualizing complex of the incidence algebra of finite regular cell complex"と"Castelnuovo-Mumford regularity for complexes and weakly Koszul modules"が,今年度に入って学術雑誌に受理された.特に前者は,受理される前に大幅な加筆を行い,組合せ論的な側面(正則胞体分割の半順序集合としての「メビウス関数」など)を強化している.
    また,今年度に得られた結果として,「アファイン半群環K[C]の被約な単項式イデアルIによる剰余環(最近では,"toric face ring"等と呼ばれるもの)の"sequentially Cohen-Macaulay"性(以下"seq.CM"と略す)は,Iに付随するpolytopal complexの位相的性質(と体Kの標数)のみによって定まる」を示したこと等が挙げられる.論文は,現在執筆中である.toric face ringのCohen-Macaulay性が位相的性質であることは(K[C]が多項式環の場合のMunkresの著名な結果の一般化であるが),20年前Stanleyによって証明されており,筆者も数年前,層の理論を用いた別証明を与えている.今回の結果は,この筆者自身の論法の発展である(Stanleyの証明は,Yuzvinskyによる"section ring"の理論の応用であるが,seq.CM性の場合に,この論法を用いるのは困難かと思われる).なお,seq.CMは,Cohen-Macaulayを一般化した概念で,近年では,"shifting"や"non-pure shellability"との関連から,「組合せ論的可換代数」での重要性が増している.

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  • Stanley-Reisner環の理論に現れるKoszul双対性の研究

    Grant number:13740011  2001 - 2002

    日本学術振興会  科学研究費助成事業 若手研究(B)  若手研究(B)

    柳川 浩二

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    Grant amount:\1800000 ( Direct Cost: \1800000 )

    私は,数年前,組合せ論的可換代数の基本的な概念である「Stanley-Reisenr環」を一般化して,「squarefree加群」を定義した.この概念は,当該分野の道具の一つとして定着しつつある.squarefree加群の有界な導来圏には,3つの「双対性」が存在し,3次対称群の3つの互換の如く作用している.この現象は,Koszul双対性(特に,Bernstein-Gel'fand-Gel'fand対応)と関連している.この研究成果は,Journal of the Mathematical Society of Japanへの掲載が決定している"Derived Category of Squarefree Modules and Local Cohomology with Monomial Ideal Support"にまとめた.(この論文の第一稿は,平成12年度に投稿したが,レフェリーの助言もあり,平成13年度に全面的に改定し,結果を大幅に強めた.また,14年度にも若干の改良を行った.この意味で,この論文は13-14年度の成果でもある.)
    Stanley-Reisener環が,対応する単体的複体の位相幾何学的性質を様々に反映しているのに対し,その一般化であるsquarefree加群の幾何学的な意味は,暫くはっきりしなかったが,平成14年度の研究で,(n変数多項式環上の)squarefree加群から,(n-1)次元閉球体上の層が構成でき,自然な(スキーム論における"Proj"と類似の)理論が展開できることが分かった.この文脈では,位相幾何学のポアンカレ・ヴェルディエ双対性と,可換代数の局所双対性が等価となる.この研究成果は,投稿中のプレプリント"Stanley-Reisner rings, sheaves, and Poincare-Verdier duality"にまとめた.

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  • 単項式イデアルの研究への圏論的手法の応用

    Grant number:12740013  2000

    日本学術振興会  科学研究費助成事業  奨励研究(A)

    柳川 浩二

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    Grant amount:\1100000 ( Direct Cost: \1100000 )

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  • Geometry of space of Riemannian manifolds

    Grant number:11640075  1999 - 2002

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    OTSU Yukio, GOTO Ryushi, SHIOYA Takashi, YAMADA Koutarou

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    Grant amount:\3600000 ( Direct Cost: \3600000 )

    Let us denote by A the space of Alexnadrov spaces of bounded curvature below and Hausdorff dimension above equipped with Hausdorff distance and by I the space of upper-semicontinuous functions on A. We call I the space of invariants. An ordered finite set of points of metric space is called a net, which is a discretization of the metric space. Since the configuration space of all nets is identified with the product of the space, the set N of pairs of spaces in A and its nets can be interpreted as a fiber space over A. We consider a map that assign the matrix of mutual distances of two points for each net. In this way we can represent N as a subspace of some Banach space. Then we introduce other maps form N to some Euclidian space that take local information of the above distance matrix. Especially we defined discrete Laplacian similar to the Laplacian of functions of Riemannian manifold. We introduced new statistical method to take average of discrete Laplacian on configuration space of nets. In this way we have showd that the eigenvalues and eigenvectors of discrete Laplacian converge to the limit independent of the choice of nets ; we also proved that coincides with the Laplacian in the sense of Kuwae-Machigashira-shioya in some sense.
    Next we defined new structure on A by comparing two discrete Laplacian of different spaces and nets because they are same member of matrix space. Since in information geometry the relative entropy of two distributions determines Reimannian metric, we first introduced stationary Markov chain form the Laplacian, then we apply the relative entropy for them; finally we construct continuum limit of them, which is a generalization of Hausdorff distance.

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  • 次数付可換環のヒルベルト関数と極小自由分解

    Grant number:09740014  1997 - 1998

    日本学術振興会  科学研究費助成事業 奨励研究(A)  奨励研究(A)

    柳川 浩二

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    Grant amount:\1800000 ( Direct Cost: \1800000 )

    97年度は、E.Ballico 氏と共同で、very strange curve と言う、ある意味で極めて病的な射影曲線を研究し、これを正標数の代数閉体上の Cohen-Macaulay 斉次整域のヒルベルト関数の研究に応用した。very strange curve の定義イデアルは基礎体の標数より小さい次数の元を殆ど含まないことを示したものである(単なる“strangecurve"では、この性質を持たない)が、未だはっきりしない部分も多く、今後も研究を継続していきたい。
    また同年度は、Bayer, Peeva, Sturmfels らによって当時導入されたばかりであった、凸幾何学的に特殊な構造を持った monomial ideal を研究し、これの準素成分がある種の「連結性」を持つことを示した(少し後で、toric ideal の initial ideal の準素成分が同様の性質を持つことが、 Hosten と Thomas によって示されている)。先行する研究が凸幾何学的手法によるものであったのに対し、筆者は、局所双対性等、可換代数的な手法も併用した。この研究は、98年度には、E.Mill,Sturmfels 両氏との共同研究に発展した(現在投稿中)。ここでは、 toric ideal の initial ideal も研究しており、手法的にも、 local h-vector や Alexander 双対性といった新しいものを導入している。
    また、98年度は、 Stanley-Reisner 環の Alezander 双対性も研究し、 Cohen-Macaulayな Stanley-Reisner 環 k[Δ] の標準加群の加群構造の情報と、その双対の Stanley-Reisner 環 k[Δ^V]の極小自由分解の(微分写像まで込めた)情報が等価であること等を示した。
    上述の monomial ideal や toric ideal の凸幾何学的自由分解の話題は、最近、Bayer,Popescu らによって(凸幾何学的にも可換代数的にも)より精密な方向に発展してきており、筆者も、この方向での研究を続けていきたいと考えている。

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  • Foundation of computational Commutative algebra with a view toward combinatorics on convex polytopes

    Grant number:09440013  1997 - 1998

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

    HIBI Takayuki, YANAGAWA Koji, NAMIKAWA Yoshinori, MIYANISHI Masayoshi, SUZUKI Takashi, KAWANAKA Noriaki

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    Grant amount:\3400000 ( Direct Cost: \3400000 )

    The important activity during the period of the present research project is, first, to present the concept of componentwise linear ideals and to establish its fundamental theory and, second, to study generic initial ideals of simplicial complexes and to discuss their concrete and effective applications to combinatorics. First of all, we obtained the theorem that the squarefree monomial ideal associated with a simplicial complex is componentwise linear if and only if its dual complex is sequentially Cohen-Macaulay, and explained the algebraic aspect of sequentially Cohen-Macaulay complexes and their h-triangles. Second, based on fundamental study about generic initial ideals of coruponentwise linear ideals, the important result that a homogeneous ideal of the polynomial ring possesses the stable Betti numbers if and only if the ideal is componentwise linear was established. Such the theorem guarantees that componentwise linear ideals will play an important role in computational commutative algebra. Third, in order to obtain sophisticated generalization of Kruskal-Katona theorem in classical combinatorics on finite sets, via the discussion on the existence of a squarefree strongly stable ideal having the same graded Betti numbers as those of the generic initial ideal of a squarefree ideal in the polynomial ring, we did succeed in obtaining the affirmative answer to the outstanding conjecture that the graded Betti numbers of a squarefree ideal with a fixed Hubert function are less than or equal to those of the lexsegment ideal.

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Social Activities

Devising educational methods

  • 1セメスターに少なくとも3回程度、レポート課題を課している。これは、「提出することに意味がある」ものではなく、丁寧に添削し、解答が間違っている場合はヒントや正解を書き込み、返却している。

Teaching materials

  • 教科書は、市販のものを使用している(所属学科のスタッフが作成した教科書も使っているが、筆者の赴任前なので、自分は執筆に関わっていいない)。自学科向けの専門科目では、教科書に載っていない題材を教えたい場合、自分で教科書・副読本風の教材を作成し、学生にプリント配布することもある。

Teaching method presentations

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Special notes on other educational activities

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