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Application of Koszul duality to commutative algebra

Research Project

Project/Area Number 19540028
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 Kouji  Kansai University, システム理工学部, 准教授 (40283006)

Co-Investigator(Kenkyū-buntansha) 和久井 道久  関西大学, システム理工学部, 専任講師 (60252574)
毛利 出  静岡大学, 理学部, 准教授 (50436903)
寺井 直樹  佐賀大学, 文化教育学部, 准教授 (90259862)
若松 隆義  埼玉大学, 教育学部, 教授 (00192435)
Co-Investigator(Renkei-kenkyūsha) TERAI Naoki  佐賀大学, 文化教育学部, 准教授 (90259862)
WAKUI Michihisa  関西大学, システム理工学部, 講師 (60252574)
MORI Izuru  静岡大学, 理学部, 准教授 (50436903)
WAKAMATSU Takayoshi  埼玉大学, 教育学部, 教授 (00192435)
Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords組合せ論的可換代数 / Stanley-Reisner環 / アファイン半群環 / 導来圏 / Koszul双対性 / 双対化複体 / 単体的半順序集合 / 局所双対性 / ポアンカレ・ヴェルディエ双対性 / toric face ring / Castelnuovo-Mumford regularity / linearity defect / dualizing complex / 石田複体
Research Abstract

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.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (23 results)

All 2010 2009 2008 2007 Other

All Journal Article (10 results) (of which Peer Reviewed: 10 results) Presentation (13 results)

  • [Journal Article] Dualizing complex of toric face ring2009

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

      Nagoya Mathematical Journal Vol.196

      Pages: 87-116

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Linearity defect and regularity over a Koszul algebra2009

    • Author(s)
      Kohji Yanagawa
    • Journal Title

      Mathematica Scandinavica Vol.104

      Pages: 205-220

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Linearity Defect and Regularity over a Koszul Algebra2009

    • Author(s)
      Kohji Yanagawa
    • Journal Title

      Mathematica Scandinavica 104

      Pages: 205-220

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Dualizing complex of a toric face ring2009

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

      Nagoya Mathematical Journal 196

      Pages: 87-116

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Linearity Defect and Regularity over a Koszul Algebra2009

    • Author(s)
      Kohji Yanagawa
    • Journal Title

      Mathematica Scandinavica (印刷中)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Notes on C-graded modules over an affine semigroup ring K[C]2008

    • Author(s)
      Kohji Yanagawa
    • Journal Title

      Communications in Algebra Vol.36

      Pages: 3122-3146

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Notes on C-graded modules over an affine semigroup ring K[C]2008

    • Author(s)
      Kohji Yanagawa
    • Journal Title

      Communications in Algebra 36

      Pages: 3122-3146

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Linearity defects of face rings2007

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

      Journal of Algebra Vol.314

      Pages: 362-382

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Linearity defects of face rings2007

    • Author(s)
      Ryota Okazaki
    • Journal Title

      Journal of Agebra 314

      Pages: 362-382

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Notes on C-graded modules over an affine semigroup ring F[C]

    • Author(s)
      Kohji Yanagawa
    • Journal Title

      Communications in Algebra (印刷中)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] On the face ring of a simplicial poset2010

    • Author(s)
      Kohji Yanagawa
    • Organizer
      The 5th joint Japan-Vietnam join seminar on Commutative algebra
    • Place of Presentation
      ハノイ数学研究所
    • Year and Date
      2010-01-08
    • Related Report
      2009 Final Research Report
  • [Presentation] On the face ring of a simplicial poset2010

    • Author(s)
      Kohji Yanagawa
    • Organizer
      The 5^<th> joint Japan-Vietnam join seminar on Commutative algebra
    • Place of Presentation
      Hsnoi Institute of Mathematics(ベトナム)
    • Year and Date
      2010-01-08
    • Related Report
      2009 Annual Research Report
  • [Presentation] Homological approach to the face ring of a simplicial poset2009

    • Author(s)
      柳川浩二
    • Organizer
      第42回環論および表現論シンポジウム
    • Place of Presentation
      大阪教育大学
    • Year and Date
      2009-10-10
    • Related Report
      2009 Annual Research Report 2009 Final Research Report
  • [Presentation] Recent topics on derived categories in combinatorial commutative algebra2009

    • Author(s)
      柳川浩二
    • Organizer
      研究集会Syzygies of Projective Varieties
    • Place of Presentation
      佐賀大学
    • Year and Date
      2009-09-15
    • Related Report
      2009 Final Research Report
  • [Presentation] Recent topics on derived categories in combinatorial commutative algebra2009

    • Author(s)
      Kohji Yanagawa
    • Organizer
      研究集会「Syzygies of Projective Varieties」
    • Place of Presentation
      佐賀大学
    • Year and Date
      2009-09-15
    • Related Report
      2009 Annual Research Report
  • [Presentation] Dualizing complex of a toric face ring2009

    • Author(s)
      Kohji Yanagawa
    • Organizer
      Pacific Rim Mathematical Association (PRIMA) Congress
    • Place of Presentation
      University of New SouthWales (シドニー)
    • Year and Date
      2009-06-09
    • Related Report
      2009 Final Research Report
  • [Presentation] Dualizing complex of a toric face ring2009

    • Author(s)
      Kohji Yanagawa
    • Organizer
      Pacific Rim Mathematical Association(PRIMA)Congress
    • Place of Presentation
      University of New South Wales(シドニー・豪)
    • Year and Date
      2009-06-09
    • Related Report
      2009 Annual Research Report
  • [Presentation] Dualizing complex of a toric face ring- Normal and non-normal cases2008

    • Author(s)
      柳川浩二
    • Organizer
      第30回可換環論シンポジウム
    • Place of Presentation
      国民宿舎虹の松原ホテル(佐賀県)
    • Year and Date
      2008-11-20
    • Related Report
      2009 Final Research Report
  • [Presentation] Dualizing complex of a toric face ring-Normal and non-normal cases2008

    • Author(s)
      Kohji Yanagawa
    • Organizer
      第30回可換環論シンポジウム
    • Place of Presentation
      国民宿舎虹の松原ホテル(佐賀県)
    • Year and Date
      2008-11-20
    • Related Report
      2008 Annual Research Report
  • [Presentation] Linearity defects of Stanley-Reisner rings2008

    • Author(s)
      Kohji Yanagawa
    • Organizer
      環論-表現論・ホモロジー代数との関連を中心に(P. Jorgensen教授の来阪に合わせて行われた研究集会)
    • Place of Presentation
      大阪府立大学
    • Year and Date
      2008-07-16
    • Related Report
      2008 Annual Research Report
  • [Presentation] Squarefree modules over a toric face ring2008

    • Author(s)
      Kohji Yanagawa
    • Organizer
      International Conference on Commutative Algebra
    • Place of Presentation
      横浜開港記念会館
    • Year and Date
      2008-03-21
    • Related Report
      2009 Final Research Report 2007 Annual Research Report
  • [Presentation] Linearity Defect and Regularity over a Koszul Algebra2007

    • Author(s)
      柳川 浩二
    • Organizer
      第29回可換環論シンポジウム
    • Place of Presentation
      愛知厚生年金会館ウェルシティなごや
    • Year and Date
      2007-11-21
    • Related Report
      2007 Annual Research Report
  • [Presentation] Regularities of cochain complexes and Koszul duality2007

    • Author(s)
      Kohji Yanagawa
    • Organizer
      Castelnuovo-Mumford Regularity and Applications
    • Place of Presentation
      マックスプランク数学研究所(ライプツィヒ)
    • Year and Date
      2007-06-15
    • Related Report
      2009 Final Research Report 2007 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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