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Hilbert function of local rings

Research Project

Project/Area Number 15K04820
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

Ozeki Kazuho  山口大学, 大学院創成科学研究科, 准教授 (70445849)

Project Period (FY) 2015-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywordsヒルベルト函数 / ヒルベルト係数 / Rees代数 / 随伴次数環 / Sally加群 / コーエン・マコ―レイ局所環 / 随伴次数間 / Cohen-Macaulay環 / 可換環論 / 巴系イデアル
Outline of Final Research Achievements

The purpose of this research is to explore the behavior of the Hilbert functions of ideals in Cohen-Macaulay local rings.
I explored the relationship between the first Hilbert coefficient and the structure of the associated graded ring of integrally closed ideals in a Cohen-Macaulay local ring.
I also gave a characterization for the almost minimal value of the first Hilbert coefficient in the case of the normal filtration in an analytically unramified Cohen-Macaulay local ring. I strongly used some structure theorems of Sally modules in these results.

Report

(4 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (19 results)

All 2018 2017 2016 2015 Other

All Int'l Joint Research (2 results) Journal Article (5 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 3 results) Presentation (12 results) (of which Int'l Joint Research: 5 results,  Invited: 7 results)

  • [Int'l Joint Research] ジェノバ大学(イタリア)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] ジェノバ大学数学科(イタリア)

    • Related Report
      2016 Research-status Report
  • [Journal Article] The structure of the Sally module of integrally closed ideals2017

    • Author(s)
      Kazuho Ozeki and Maria Evelina Rossi
    • Journal Title

      Nagoya Mathematical Journal

      Volume: 227 Pages: 49-76

    • DOI

      10.1017/nmj.2016.47

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] The structure of the Sally modules of integrally closed ideals2017

    • Author(s)
      Kazuho Ozeki
    • Journal Title

      Proceedings of the 49th Symposium on Ring Theory and Representation Theory

      Volume: - Pages: 135-142

    • Related Report
      2016 Research-status Report
  • [Journal Article] The first Hilbert coefficient and Buchsbaumness of associated graded rings2017

    • Author(s)
      Kazuho Ozeki
    • Journal Title

      第38回可換環論シンポジウム報告集

      Volume: - Pages: 152-161

    • Related Report
      2016 Research-status Report
  • [Journal Article] Sectional genera of parameter ideals2016

    • Author(s)
      Shiro Goto and Kazuho Ozeki
    • Journal Title

      Journal of Algebra

      Volume: 446 Pages: 58-76

    • DOI

      10.1016/j.jalgebra.2015.09.005

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] The second Hilbert coefficients and the homological torsions of parameters2015

    • Author(s)
      Shiro Goto, Kazuho Ozeki
    • Journal Title

      Journal of Pure and Applied Algebra

      Volume: 219 Issue: 5 Pages: 1685-1703

    • DOI

      10.1016/j.jpaa.2014.07.006

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Presentation] A study of the second normal Hilbert coefficient2018

    • Author(s)
      Kazuho Ozeki
    • Organizer
      Mini-Workshop on Commutative Algebra, 北海道教育大学札幌駅前サテライト(北海道札幌市)
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] The structure of the Sally modules of integrally closed ideals2017

    • Author(s)
      Kazuho Ozeki
    • Organizer
      Algebra & Geometry Seminar
    • Place of Presentation
      Genova University (Genova, Italy)
    • Year and Date
      2017-03-22
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] The first Hilbert coefficient and Buchsbaumness of associated graded rings2017

    • Author(s)
      Kazuho Ozeki
    • Organizer
      International Workshop on Commutative Algebra
    • Place of Presentation
      Thai Nguyen University (Thai Nguyen, Vietnam)
    • Year and Date
      2017-01-05
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Almost minimal normal Hilbert coefficients2017

    • Author(s)
      Kazuho Ozeki
    • Organizer
      International Conference on Commutative Algebra and its interaction to Combinatorics, Discrete Geometry and Singularity Theory, Hanoi and Ha Long (Vietnam)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Almost minimal normal Hilbert coefficients2017

    • Author(s)
      Kazuho Ozeki
    • Organizer
      International School and Workshop on Commutative Algebra, Ton Duc Thang University, Ho Chi Minh City (Vietnam)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] The first Hilbert coefficient and Buchsbaumness of associated graded rings2016

    • Author(s)
      Kazuho Ozeki
    • Organizer
      第38回可換環論シンポジウム
    • Place of Presentation
      IPC生産性国際交流センター(神奈川県葉山市)
    • Year and Date
      2016-11-21
    • Related Report
      2016 Research-status Report
  • [Presentation] The first two Hilbert coefficients and Buchsbaumness of associated graded rings2016

    • Author(s)
      Kazuho Ozeki
    • Organizer
      Japan-Vietnam Workshop on Commutative Algebra, -by and for young mathematicians- Local rings Combinatorics, and Representation Theory
    • Place of Presentation
      明治大学生田キャンパス(神奈川県川崎市)
    • Year and Date
      2016-09-19
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] The structure of the Sally modules of integrally closed ideals2016

    • Author(s)
      Kazuho Ozeki
    • Organizer
      The 49th Symposium on Ring Theory and Representation Theory
    • Place of Presentation
      大阪府立大学中百舌鳥キャンパス(大阪府堺市)
    • Year and Date
      2016-08-31
    • Related Report
      2016 Research-status Report
  • [Presentation] 整閉イデアルのSally加群の構造について2016

    • Author(s)
      大関一秀
    • Organizer
      2016年度日本数学会年会
    • Place of Presentation
      筑波大学(茨城県つくば市)
    • Year and Date
      2016-03-16
    • Related Report
      2015 Research-status Report
  • [Presentation] The structure of the Sally modules and the first Hilbert coefficient of ideals2016

    • Author(s)
      Kazuho Ozeki
    • Organizer
      Workshop on Commutative Algebra- Part II, Local Algebra and Representation Theory-
    • Place of Presentation
      VIASM's villa (Tuan Chau, Vietnam)
    • Year and Date
      2016-01-06
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] The structure of the Sally module of integrally closed ideals2015

    • Author(s)
      大関一秀
    • Organizer
      Ring Theory and Representation Theory Seminar
    • Place of Presentation
      名古屋大学多元数理科学研究科(愛知県名古屋市)
    • Year and Date
      2015-12-14
    • Related Report
      2015 Research-status Report
  • [Presentation] The structure of the filtration of Sally modules2015

    • Author(s)
      Kazuho Ozeki and Maria Evelina Rossi
    • Organizer
      第37回可換環論シンポジウム
    • Place of Presentation
      倉敷シーサイドホテル(岡山県倉敷市)
    • Year and Date
      2015-11-20
    • Related Report
      2015 Research-status Report

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Published: 2015-04-16   Modified: 2019-03-29  

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