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

Research Project

Project/Area Number 26400049
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionSaga University

Principal Investigator

Terai Naoki  佐賀大学, 教育学部, 教授 (90259862)

Co-Investigator(Kenkyū-buntansha) 庄田 敏宏  佐賀大学, 教育学部, 准教授 (10432957)
岡田 拓三  佐賀大学, 工学(系)研究科(研究院), 准教授 (20547012)
宮崎 誓  熊本大学, 教育学部, 教授 (90229831)
青山 崇洋  佐賀大学, 教育学部, 准教授 (60516178)
Co-Investigator(Renkei-kenkyūsha) YOSHIDA KENICHI  日本大学, 文理学部, 教授 (80240802)
YANAGAWA KOUJI  関西大学, 工学部, 教授 (40283006)
KIMURA KYOUKO  静岡大学, 大学院理学研究科, 助教 (60572633)
Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords辺イデアル / 射影次元 / 記号的べき / Stanley-Reisnerイデアル / Stanley-Reisner イデアル / 算術階数
Outline of Final Research Achievements

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.

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (4 results)

All 2017 2016 2015 2014

All Journal Article (3 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 3 results,  Acknowledgement Compliant: 2 results,  Open Access: 1 results) Presentation (1 results) (of which Int'l Joint Research: 1 results,  Invited: 1 results)

  • [Journal Article] Stanbility of depths of symbolic powers of Stanley-Reisner ideals2017

    • Author(s)
      Le Tuan Hoa, Kyouko Kimura, Naoki Terai, Trung Tran Nam
    • Journal Title

      Journal of Algebra

      Volume: 473 Pages: 307-323

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Arithmetical rank of a squarefree monomial ideal whose Alexander dual is of deviation two2015

    • Author(s)
      Kyouko Kimura, Naoki Terai, Ken-ichi Yoshida
    • Journal Title

      Acta Mathematica Vietnamica

      Volume: 40 Issue: 3 Pages: 375-391

    • DOI

      10.1007/s40306-015-0136-x

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] On the associated primes and the depth of the second power of sqarefree monomial ideals2014

    • Author(s)
      Naoki Terai, Ngo Viet Trung
    • Journal Title

      Journal of Pure and Applied Algebra

      Volume: 218 Issue: 6 Pages: 1117-1129

    • DOI

      10.1016/j.jpaa.2013.11.008

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Presentation] Licci squarefree monomial ideals2016

    • Author(s)
      Naoki Terai
    • Organizer
      International Conference and the 8th Japan-Vietnam Joint Seminar on Commutative Algebra
    • Place of Presentation
      Ha Long, Vietnam
    • Year and Date
      2016-03-21
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited

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Published: 2014-04-04   Modified: 2018-03-22  

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