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Application of commutative algebra to topological study on affine oriented matroids

Research Project

Project/Area Number 16K05114
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
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, 教授 (40283006)

Project Period (FY) 2016-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords組合せ論的可換代数 / アファイン有向マトロイド / Cohen-Macaulay 性 / Cohen-Macaulay性 / Specht ideal / コーエン・マコーレー環 / 極小自由分解 / Cohen-Macaulay性
Outline of Final Research Achievements

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.

Academic Significance and Societal Importance of the Research Achievements

数学の基礎研究であり、基本的には純粋な学術的価値を追求するものである。たとえば、主たる目的とした予想は、かつて「Zaslavsky予想」と呼ばれた比較的有名な問題(現在は、Dong によって解決されている)の一般化を図るものであった。
ただ、有向マトロイドは応用数学の範疇に属する研究対象であり、今回の結果は純粋数学からのアプローチではあるが、将来的・間接的には何らかの応用が見つかる可能性が有る。

Report

(5 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (10 results)

All 2020 2019 2018 2017 2016

All Journal Article (5 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 5 results,  Acknowledgement Compliant: 1 results) Presentation (5 results) (of which Int'l Joint Research: 2 results,  Invited: 2 results)

  • [Journal Article] When is a Specht ideal Cohen-Macaulay?2020

    • Author(s)
      Kohji Yanagawa
    • Journal Title

      Journal of Commutative Algebra

      Volume: 掲載決定

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Vandermonde determinantal ideals2019

    • Author(s)
      Junzo Watanabe, Kohji Yanagawa
    • Journal Title

      Mathematica Scandinavica

      Volume: 掲載決定

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] The Cohen-Macaulayness of the bounded complex of an affine oriented matroid2018

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

      Journal of Combinatorial Theory, Series A

      Volume: 157 Pages: 1-27

    • DOI

      10.1016/j.jcta.2018.01.004

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Lyubeznik numbers of local rings and linear strands of graded ideals2017

    • Author(s)
      Alvarez Montaner Josep、Yanagawa Kohji
    • Journal Title

      Nagoya Mathematical Journal

      Volume: 掲載決定 Pages: 23-54

    • DOI

      10.1017/nmj.2017.10

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Non-level semi-standard graded Cohen-Macaulay domain with h-vector (h_0,h_1,h_2)2017

    • Author(s)
      Akihiro Higashitani, Kohji Yanagawa
    • Journal Title

      J Pure Appl. Algebra

      Volume: 印刷中 Issue: 1 Pages: 191-201

    • DOI

      10.1016/j.jpaa.2017.03.011

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] When is a Specht ideal Cohen-Macaulay?2019

    • Author(s)
      Kohji Yanagawa
    • Organizer
      1147th AMS Meeting, Spring Central and Western Joint Sectional Meeting, Special Session on Commutative Algebra and its Environs,
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Strongly stable ideal の既約分解と局所コホモロジーの関係2019

    • Author(s)
      柴田 孝祐; 柳川 浩二
    • Organizer
      日本数学会 2019年度年会 代数学分科会
    • Related Report
      2018 Research-status Report
  • [Presentation] Strongly stable ideal のalternative polarization とそのAlexander 双対 について2018

    • Author(s)
      柴田 孝祐; 柳川 浩二
    • Organizer
      日本数学会 秋季総合分科会 代数学分科会
    • Related Report
      2018 Research-status Report
  • [Presentation] When is a Specht ideal Cohen-Macaulay?2017

    • Author(s)
      柳川浩二
    • Organizer
      PRIMA(Pacific Rim Mathematical Association) 2017 Congress
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Non-level semi-standard graded Cohen-Macaulay domains with h-vectors (h_0, h_1, h_2)2016

    • Author(s)
      東谷 章弘, 柳川 浩二
    • Organizer
      日本数学会 秋季総合分科会
    • Place of Presentation
      関西大学
    • Year and Date
      2016-09-16
    • Related Report
      2016 Research-status Report

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Published: 2016-04-21   Modified: 2021-02-19  

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