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

Research Project

Project/Area Number 22540057
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionKansai University

Principal Investigator

YANAGAWA Kohji  関西大学, システム理工学部, 准教授 (40283006)

Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords組合せ論的可換代数 / Borel fixed ideal / 極小自由分解 / 双対化複体 / アファイン半群環 / affine semigroup ring / toric face ring / 離散モース理論 / 単項式イデアル / (単項式イデアルの)polarization / Stanley depth / 局所双対性
Research Abstract

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.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (25 results)

All 2013 2012 2011 2010 Other

All Journal Article (9 results) (of which Peer Reviewed: 8 results) Presentation (16 results) (of which Invited: 1 results)

  • [Journal Article] Alternative polarizations of Borel fixed ideals, Eliahou.Kervaire type resolution and discrete Morse theory2013

    • Author(s)
      Ryota Okazaki and Kohji Yanagawa
    • Journal Title

      Journal of Algebraic Combinatorics

      Volume: 掲載決定

    • Related Report
      2012 Final Research Report
  • [Journal Article] Alternative polarizations of Borel fixed ideals, Eliahou-Kervaire type resolution and discrete Morse theory2013

    • Author(s)
      Ryota Okazaki
    • Journal Title

      Journal of Algebraic Combinatorics

      Volume: 印刷中

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Alternative polarizations of Borel fixed ideals2012

    • Author(s)
      Kohji Yanagawa
    • Journal Title

      Nagoya Mathematical Journal

      Volume: Vol. 207 Pages: 79-93

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Sliding functor and polarization functor for multigraded modules2012

    • Author(s)
      Kohji Yanagawa
    • Journal Title

      Communications in Algebra

      Volume: Vol. 40 Pages: 1151-1166

    • Related Report
      2012 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Alexander duality and Stanley depth of multigraded modules2011

    • Author(s)
      Ryota Okazaki and Kohji Yanagawa
    • Journal Title

      Journal of Algebra

      Volume: Vol. 340, Pages: 35-52

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Higher Cohen-Macaulay property of squarefree modules and simplicial posets2011

    • Author(s)
      Kohji Yanagawa
    • Journal Title

      Proceedings of the American Mathematical Society

      Volume: Vol. 139 Pages: 3057-3066

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Dualizing complex of the face ring of a simplicial poset2011

    • Author(s)
      Kohji Yanagawa
    • Journal Title

      Journal of Pure and Applied Algebra

      Volume: Vol. 215 Pages: 2231-2241

    • Related Report
      2012 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Alexander duality and Stanley depth of multigraded modules2011

    • Author(s)
      Ryota Okazaki
    • Journal Title

      Journal of Algebra

      Volume: 340 Issue: 1 Pages: 36-62

    • DOI

      10.1016/j.jalgebra.2011.05.028

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Higher Cohen-Macaulay property of squarefree modules and simplicial posets2011

    • Author(s)
      Koji Yanagawa
    • Journal Title

      Proceedings of the American Mathematical Society

      Volume: 139 Pages: 3057-3066

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Dualizing complexes of seminormal affine semigroup rings and toric face rings2012

    • Author(s)
      柳川浩二
    • Organizer
      第34回可換環論シンポジウム
    • Place of Presentation
      湘南国際村 生産性国際交流センター
    • Year and Date
      2012-11-25
    • Related Report
      2012 Final Research Report
  • [Presentation] On a minimal free resolution of a Borel fixed ideal and its supporting CW complex2012

    • Author(s)
      岡崎亮太, 柳川浩二
    • Organizer
      日本数学会 秋季総合分科会 代数学分科会
    • Place of Presentation
      九州大学
    • Year and Date
      2012-09-21
    • Related Report
      2012 Final Research Report
  • [Presentation] Free resolutions of (variants of) Borel fixed ideals2012

    • Author(s)
      柳川浩二
    • Organizer
      第52回 代数学シンポジウム
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2012-08-21
    • Related Report
      2012 Final Research Report
  • [Presentation] Discrete Morse theory and combinatorial commutative algebra II2012

    • Author(s)
      柳川浩二
    • Organizer
      (非)可換代数とトポロジー
    • Place of Presentation
      信州大学(招待講演)
    • Year and Date
      2012-03-15
    • Related Report
      2011 Annual Research Report
  • [Presentation] Alternative polarizations of Borel fixed ideals, Eliahou-Kervaire type resolution and discrete Morse theory2011

    • Author(s)
      Kohji Yanagawa
    • Organizer
      The 7th Japan-Vietnam Joint Seminar on Commutative Algebra
    • Place of Presentation
      クイニョン大学(ベトナム)研究所
    • Year and Date
      2011-12-16
    • Related Report
      2012 Final Research Report
  • [Presentation] Alternative polarizations of Borel fixed ideals, Eliahou-Kervaire type resolution and discrete Morse theory2011

    • Author(s)
      Kohji Yanagawa
    • Organizer
      The 7th Japan-Vietnam Joint Seminar on Commutative Algebra
    • Place of Presentation
      クイニョン大学(ベトナム)(招待講演)
    • Year and Date
      2011-12-16
    • Related Report
      2011 Annual Research Report
  • [Presentation] Alternative polarizations of Borel fixed ideals, Eliahou-Kervaire type resolution2011

    • Author(s)
      Ryota Okazaki
    • Organizer
      第33回可換環論シンポジウム
    • Place of Presentation
      浜名湖カアッタ(静岡県)
    • Year and Date
      2011-11-10
    • Related Report
      2011 Annual Research Report
  • [Presentation] Alternative polarizations of Borel fixed ideals and Eliahou-Kervaire type resolutions2011

    • Author(s)
      岡崎亮太, 柳川浩二
    • Organizer
      第44回環論および表現論シンポジウム
    • Place of Presentation
      岡山大学
    • Year and Date
      2011-09-27
    • Related Report
      2012 Final Research Report
  • [Presentation] Alternative polarizations of Borel fixed ideals, Eliahou-Kervaire type resolution2011

    • Author(s)
      Ryota Okazaki
    • Organizer
      第44回環論および表現論シンポジウム
    • Place of Presentation
      岡山大学
    • Year and Date
      2011-09-27
    • Related Report
      2011 Annual Research Report
  • [Presentation] Derived categories and topological methods in combinatorial commutative algebra I, II2011

    • Author(s)
      柳川浩二
    • Organizer
      空間の代数的・幾何的モデルとその周辺
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Final Research Report
  • [Presentation] Derived categories and topological methods in combinatorial commutative algebra I, II2011

    • Author(s)
      柳川浩二
    • Organizer
      空間の代数的・幾何的モデルとその周辺
    • Place of Presentation
      京都大学数理解析研究所(招待講演)
    • Related Report
      2011 Annual Research Report
  • [Presentation] Sliding functor and polarization functor for multigraded modules2010

    • Author(s)
      Kohji Yanagawa
    • Organizer
      The 6th Japan-Vietnam Joint Seminar on Commutative Algebra
    • Place of Presentation
      湘南国際村 生産性国際交流センター
    • Year and Date
      2010-12-13
    • Related Report
      2012 Final Research Report
  • [Presentation] Sliding functor and polarization functor for multigraded modules2010

    • Author(s)
      Kohji Yanagawa
    • Organizer
      The 6^<th> Japan-Vietnam Joint Seminar on Commutative Algebra
    • Place of Presentation
      IPC生産性国際交流センター(神奈川県)
    • Year and Date
      2010-12-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] Derived categories in combinatorial commutative algebra2010

    • Author(s)
      Kohji Yanagawa
    • Organizer
      研究集会"Lefschetz fibration and category theory"
    • Place of Presentation
      大阪大学(招待講演)
    • Year and Date
      2010-06-04
    • Related Report
      2010 Annual Research Report
  • [Presentation] Free resolutions of (variants of) Borel fixed ideals

    • Author(s)
      柳川浩二
    • Organizer
      第57回代数学シンポジウム
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Dualizing complexes of seminormal affine semigroup rings and toric face rings

    • Author(s)
      柳川浩二
    • Organizer
      第34回可換環論シンポジウム
    • Place of Presentation
      IPC生産性国際センター
    • Related Report
      2012 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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