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Research of multiplier ideals and tight closures from viewpoint of commutative algebra and computational algebra

Research Project

Project/Area Number 19340005
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

YOSHIDA Ken-ichi  Nagoya University, 大学院・多元数理科学研究科, 准教授 (80240802)

Co-Investigator(Kenkyū-buntansha) HASHIMOTO Mitsuyasu  名古屋大学, 大学院・多元数理科学研究科, 准教授 (10208465)
IYAMA Osamu  名古屋大学, 大学院・多元数理科学研究科, 教授 (70347532)
FUJINO Osamu  名古屋大学, 大学院・多元数理科学研究科, 准教授 (60324711)
寺井 直樹  佐賀大学, 文化教育学部, 准教授 (90259862)
Co-Investigator(Renkei-kenkyūsha) TERAI Naoki  佐賀大学, 文化教育学部, 准教授 (90259862)
Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥8,450,000 (Direct Cost: ¥6,500,000、Indirect Cost: ¥1,950,000)
Fiscal Year 2009: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2008: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2007: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Keywords乗数イデアル / 密着閉包 / F正則性 / 正則局所環 / コーエン・マコーレー性 / スタンレー・リースナー環 / グラフ / 算術的階数 / テストイデアル / エッジイデアル / 完全交叉 / マコーレー性 / スタンレー・リースナーイデアル / Hilbert-Kunz重複度 / グラフイデアル / Stanley-Reisner環 / 形式的冪 / Buchsbaum環 / 判定イデアル / 特異点 / 局所化 / 完備化
Research Abstract

The leader of this research introduced the notion of a generalized tight closure and succeeded to redefine multiplier ideals in terms of commutative ring theory. Precisely speaking, the multiplier ideal is given as the limit of generalized test ideals. In this research, we found several differences between the behavior of test ideals and that of multiplier ideals. Moreover, we extended the theory of test ideals in order to study several invariants in the theory of commutative algebra.

Report

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

    (56 results)

All 2010 2009 2008 2007 Other

All Journal Article (36 results) (of which Peer Reviewed: 29 results) Presentation (17 results) Remarks (3 results)

  • [Journal Article] Locally complete intersection of Stanley-Reisner ideals2009

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

      Illinois J. Math 53

      Pages: 413-429

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Test ideals vs. multiplier ideals2009

    • Author(s)
      M. Mustata, Ken-ichi Yoshida
    • Journal Title

      Nagoya Math. J Vol.193

      Pages: 1-18

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Arithmetical rank of squarefree monomial ideals with small arithmetic degree2009

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

      J. Alg. Combinatorics Vol.29

      Pages: 389-404

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Arithmetical rank of monomial ideals of deviation two, in2009

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

      Contemporary Mathematics Vol.502

      Pages: 73-112

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Cluster structures for 2-Calabi-Yau categories and unipotent groups2009

    • Author(s)
      Osamu Iyama, I. Reiten, J. Scott
    • Journal Title

      Compos. Math 145,no.4

      Pages: 1035-1079

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Cohen-Macaulayness for symbolic power ideals of edge ideals2009

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

      第31回可換環論シンポジウム報告集

      Pages: 34-39

    • Related Report
      2009 Final Research Report
  • [Journal Article] F-purity of homomorphism, strong F-regularity, and F-injectivity2009

    • Author(s)
      Mitsuyasu Hashimoto
    • Journal Title

      第31回可換環論シンポジウム報告集

      Pages: 9-16

    • Related Report
      2009 Final Research Report
  • [Journal Article] deal-adic tight closureの局所化について2009

    • Author(s)
      吉田健一
    • Journal Title

      第21回可換環論セミナー報告集

      Pages: 1-8

    • Related Report
      2009 Final Research Report
  • [Journal Article] edge idealの冪のCohen-Macaulay性について2009

    • Author(s)
      寺井直樹, 吉田健一
    • Journal Title

      第21回可換環論セミナー報告集

      Pages: 1-8

    • Related Report
      2009 Final Research Report
  • [Journal Article] Test ideals vs. multiplier ideals2009

    • Author(s)
      K.Yoshida, M.Mustata
    • Journal Title

      Nagoya Math.J. 193

      Pages: 1-18

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Arithmetical rank of squarefree monomial ideals with small arithmetic degree2009

    • Author(s)
      K.Kimura, N.Terai, K.Yoshida
    • Journal Title

      J.Alg.Combinatorics 29

      Pages: 389-404

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Locally complete intersection of Stanley--Reisner ideals2009

    • Author(s)
      N.Terai, K.Yoshida
    • Journal Title

      Illinois J.Math. 53

      Pages: 413-429

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Test ideals vs. multiplier ideals2009

    • Author(s)
      Mircea Mustata, Ken-ichi Yoshida
    • Journal Title

      Nagoya Mathematical Journal (to appear) 193

      Pages: 1-18

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A note on Cohen-Macaulayness of Stanley-Reisner rings with Serre's condition (S2)2008

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

      Comm. Algebra Vol.36

      Pages: 464-477

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Generalized test ideals and symbolic powers2008

    • Author(s)
      S. Takagi, Ken-ichi Yoshida
    • Journal Title

      Michigan Math. J Vol.57

      Pages: 711-724

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Local cohomology on diagrams of schemes2008

    • Author(s)
      Mitsuyasu Hashimoto, M. Ohtani
    • Journal Title

      Michigan Math. J 57

      Pages: 383-425

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Acyclicity of complexes of flat modules2008

    • Author(s)
      Mitsuyasu Hashimoto
    • Journal Title

      Nagoya Math. J 192

      Pages: 111-118

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Auslander-Reiten theory revisited, Trends in representation theory of algebras and related topics2008

    • Author(s)
      Osamu Iyama
    • Journal Title

      EMS Ser. Congr. Rep., Eur. Math. Soc., Zurich

      Pages: 349-397

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Idun Fomin-Zelevinsky mutation and tilting modules over Calabi-Yau algebras2008

    • Author(s)
      Osamu Iyama, I. Reiten
    • Journal Title

      Amer. J. Math 130

      Pages: 1087-1149

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Idun Cluster tilting for one-dimensional hypersurface singularities2008

    • Author(s)
      I. Burban, Osamu Iyama, B. Keller, I. Reiten
    • Journal Title

      Adv. Math 217

      Pages: 2443-2484

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Mutation in triangulated categories and rigid Cohen-Macaulay modules2008

    • Author(s)
      Osamu Iyama, Y. Yoshino
    • Journal Title

      Invent. Math 172,no.1

      Pages: 117-168

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A note on Cohen-Macaulayness of Stanley -Reisner rings with Serre'scondition (S2)2008

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

      Communications in Algebra 36

      Pages: 464-477

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalized test ideals and symbolic powers2008

    • Author(s)
      Shunsuke Takagi, Ken-ichi Yoshida
    • Journal Title

      Michigan Mathematical Journal 57

      Pages: 711-724

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalized test ideals and symbolic powers2008

    • Author(s)
      Shunsuke Takagi, Ken-ichi Yoshida
    • Journal Title

      Michigan Math. J. (to appear) 57

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Buchsbaum homogeneous algebras with minimal multiplicity2007

    • Author(s)
      S. Goto, Ken-ichi Yoshida
    • Journal Title

      J. Pure Appl. Alg Vol.210

      Pages: 735-749

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Base change of invariant subrings2007

    • Author(s)
      Mitsuyasu Hashimoto
    • Journal Title

      Nagoya Math. J 186

      Pages: 165-171

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Auslander type conditions and cotorsion pairs2007

    • Author(s)
      Z. Huang, Osamu Iyama
    • Journal Title

      J. Algebra 318

      Pages: 93-100

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] uslander correspondence2007

    • Author(s)
      Osamu Iyama
    • Journal Title

      Adv. Math 210

      Pages: 51-82

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Higher-dimensional Auslander-Reiten theory on maximal orthogonal subcategories2007

    • Author(s)
      Osamu Iyama
    • Journal Title

      Adv. Math 210

      Pages: 22-50

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stanley-Reisner ideals which are complete intersection locally2007

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

      第29回可換環論シンポジウム報告集

      Pages: 9-18

    • Related Report
      2009 Final Research Report
  • [Journal Article] Arithmetical rank of squarefree monomial ideals, Arc Spaces and Multiplier ideals2007

    • Author(s)
      木村杏子, 寺井直樹, 吉田健一
    • Journal Title

      数理解析研究所講究録 1562

      Pages: 104-113

    • Related Report
      2009 Final Research Report
  • [Journal Article] Ideal-adic tight closure and its applications, Arc Spaces and Multiplier ideals2007

    • Author(s)
      吉田健一
    • Journal Title

      数理解析研究所講究録 1550

      Pages: 64-88

    • NAID

      110006246487

    • Related Report
      2009 Final Research Report
  • [Journal Article] Buchsbaum homogeneous algebras with minimal multiplicity2007

    • Author(s)
      Shiro Goto, Ken-ichi Yoshida
    • Journal Title

      J. Pure Appl. Alg. 210

      Pages: 735-749

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A note on Cohen-Macaulayness of Stanley-Reisner rings with Serre'scondition (S2)2007

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

      Comm. Alg. 36

      Pages: 464-477

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Effective Cowsik-Nori theorem for edge ideals, to appear in

    • Author(s)
      M. Crupi, G. Rinaldo, Naoki Terai, Ken-ichi Yoshida
    • Journal Title

      Comm. in Algebra

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Diagonal F-threshols on binomial hypersurfaces, to appear in

    • Author(s)
      M. Ohtani, K. Matsuda, Ken-ichi Yoshida
    • Journal Title

      Comm. in Algebra

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Presentation] squarefree monomial idealのべきについて2010

    • Author(s)
      寺井直樹, 吉田健一
    • Organizer
      第22回可換環論セミナー
    • Place of Presentation
      松本市中央公民館
    • Year and Date
      2010-02-03
    • Related Report
      2009 Final Research Report
  • [Presentation] Cohen-Macaulayness for symbolic power ideals of edge ideals2009

    • Author(s)
      寺井直樹, 吉田健一
    • Organizer
      第31回可換環論シンポジウム
    • Place of Presentation
      ホテルアウィーナ大阪(大阪府)
    • Year and Date
      2009-11-26
    • Related Report
      2009 Final Research Report
  • [Presentation] On Cowsik-Nori theorem for Stanley-Reisner ideals and edge ideals2009

    • Author(s)
      吉田健一
    • Organizer
      1 Prima Congress
    • Place of Presentation
      University of New South Wales(シドニー, オーストラリア)
    • Year and Date
      2009-07-06
    • Related Report
      2009 Final Research Report
  • [Presentation] On Cowsik-Nori theorem for Stanley-Reisner ideals and edge ideals2009

    • Author(s)
      K.Yoshida
    • Organizer
      1^<st> Prima Congress
    • Place of Presentation
      University of New South Wales
    • Year and Date
      2009-07-06
    • Related Report
      2009 Annual Research Report
  • [Presentation] Small Hilbert-Kunz multi-plicity and (A1)-type singularity2009

    • Author(s)
      吉田健一
    • Organizer
      The 4th Japan-Vietnam joint seminar on commutative algebra
    • Place of Presentation
      明治大学理工学部(神奈川県)
    • Year and Date
      2009-02-20
    • Related Report
      2009 Final Research Report
  • [Presentation] Small Hilbert-Kunz multiplicity and (Al) type singularity2009

    • Author(s)
      吉田健一
    • Organizer
      The 4^<th> Japan-Vietnam. Joint Seminar on Commutative Algebra
    • Place of Presentation
      明治大学
    • Year and Date
      2009-02-20
    • Related Report
      2008 Annual Research Report
  • [Presentation] edge idealの巾のCohen-Macaulay性について2009

    • Author(s)
      寺井直樹, 吉田健一
    • Organizer
      第21回可換環論セミナー
    • Place of Presentation
      釧路生涯学習センター(北海道)
    • Year and Date
      2009-01-28
    • Related Report
      2009 Final Research Report
  • [Presentation] ideal-adic tight closureの局所化について2009

    • Author(s)
      吉田健一
    • Organizer
      第21回可換環論セミナー
    • Place of Presentation
      釧路生涯学習センター(北海道)
    • Year and Date
      2009-01-27
    • Related Report
      2009 Final Research Report
  • [Presentation] Cohen-Macaulayness of symbolic powers of edge ideals of disjoint union of complete graphs2009

    • Author(s)
      吉田健一
    • Organizer
      日大セミナー
    • Place of Presentation
      日本大学文理学部(東京都)
    • Year and Date
      2009-01-19
    • Related Report
      2009 Final Research Report
  • [Presentation] 算術次数がイニシャル次数より2だけ大きいsquarefree monomial idealの算術階数について2008

    • Author(s)
      木村杏子, 寺井直樹, 吉田健一
    • Organizer
      日本数学会代数学分科会
    • Place of Presentation
      近畿大学(大阪府)
    • Year and Date
      2008-03-24
    • Related Report
      2009 Final Research Report
  • [Presentation] Some properties of generalized test ideals2008

    • Author(s)
      吉田健一
    • Organizer
      International conference on Yokohama
    • Place of Presentation
      横浜開港記念会館(神奈川県)
    • Year and Date
      2008-03-18
    • Related Report
      2009 Final Research Report
  • [Presentation] Some properties of generalized test ideals2008

    • Author(s)
      吉田 健一
    • Organizer
      International conference on Yokohama
    • Place of Presentation
      横浜開港記念会館(横浜)
    • Year and Date
      2008-03-18
    • Related Report
      2007 Annual Research Report
  • [Presentation] A note on Schmitt-Vogel lemma2008

    • Author(s)
      木村杏子, 寺井直樹, 吉田健一
    • Organizer
      数理研短期共同研究「代数、言語のアルゴリズムと計算理論」
    • Place of Presentation
      京都大学数理解析研究所(京都府)
    • Year and Date
      2008-02-22
    • Related Report
      2009 Final Research Report
  • [Presentation] Asymptotic behavior of certain squarefree monomial ideals2007

    • Author(s)
      吉田健一
    • Organizer
      quarefree monomial ideals, The Third Japan Vietnam joint seminar
    • Place of Presentation
      Institute of Mathematics (ハノイ, ベトナム)
    • Year and Date
      2007-12-03
    • Related Report
      2009 Final Research Report
  • [Presentation] (12)寺井直樹, 吉田健一, Stanley-Reisner ideals which are complete intersections locally2007

    • Author(s)
      寺井直樹, 吉田健一
    • 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(愛知県)
    • Year and Date
      2007-11-19
    • Related Report
      2009 Final Research Report
  • [Presentation] Any ideal in an F-finite RLR is a test ideal2007

    • Author(s)
      吉田健一
    • Organizer
      日本数学会代数学分科会
    • Place of Presentation
      玉大学理学部(埼玉県)
    • Year and Date
      2007-03-28
    • Related Report
      2009 Final Research Report
  • [Presentation] rithmetical rank of squarefree monomial ideals, RIMS共同研究代数、形式言語2007

    • Author(s)
      木村杏子, 寺井直樹, 吉田健一
    • Organizer
      計算システム理論とその応用
    • Place of Presentation
      京都大学数理解析研究所(京都府)
    • Year and Date
      2007-02-20
    • Related Report
      2009 Final Research Report
  • [Remarks]

    • URL

      http://kenpro.mynu.jp:8001/Profiles/0004/0000497/profile.html

    • Related Report
      2009 Final Research Report
  • [Remarks]

    • URL

      http://kenpro.mynu.jp:8001/Profiles/0004/0000497/profile.html

    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://kenpro.mynu.jp:8001/Profiles/0004/0000497/profile.html

    • Related Report
      2008 Annual Research Report

URL: 

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

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