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2012 Fiscal Year Final Research Report

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

Research Project

  • PDF
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
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
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.

  • Research Products

    (13 results)

All 2013 2012 2011 2010

All Journal Article (6 results) (of which Peer Reviewed: 5 results) Presentation (7 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

  • [Journal Article] Alternative polarizations of Borel fixed ideals2012

    • Author(s)
      Kohji Yanagawa
    • Journal Title

      Nagoya Mathematical Journal

      Volume: Vol. 207 Pages: 79-93

    • 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.

    • 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

    • 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

    • 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

    • 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
  • [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
  • [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
  • [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
    • Year and Date
      20110907-08
  • [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
  • [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
  • [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

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Published: 2014-08-29  

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