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Clarifying the basic theory of USD-sequences and their applications to the Kawasaki's theory of Macaulayfications

Research Project

Project/Area Number 17540051
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionHimeji Dokkyo University

Principal Investigator

YAMAGISHI Kikumichi  Himeji Dokkyo University, 経済情報学部, 教授 (10200601)

Co-Investigator(Kenkyū-buntansha) KAWASAKI Takeshi  首都大学東京, 都市教養学部, 助手 (40301410)
Project Period (FY) 2005 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥3,720,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥420,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2006: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2005: ¥1,200,000 (Direct Cost: ¥1,200,000)
KeywordsUSD列 / Macaulay化 / 川崎理論 / 拡大随伴次数加群 / Buchsbaum性 / FLC性 / Hilbert係数 / Sally加群 / 列性質 / P-standard列 / dd-列 / Northcottの不等式 / 成田の正定値性定理
Research Abstract

USD列の基礎理論を応用することで,極大準素イデアルのHilbert係数に関する古典論であるNorthcottの不等式やe_2に関する成田の正定値性定理の証明をSally加群を用いて簡素化するとともに,これらの定理をFLC環上に拡張した。また,極大準素ideal, I,と自然数αに対し,随伴次数付き環の概念を拡張して次数付き加群G'_α (I) を定義し,equi-I-invariantの場合,基礎環がBuchsbaum(若しくはquasi-Buchsbaum)であれば,G'_α(I)はすべてのα>0に対して基礎環と同じ性質を持つこと,Iが極大idealの場合には逆も成立すること,などを解明した。

Report

(5 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • Research Products

    (9 results)

All 2008 2007 2006 2005

All Journal Article (2 results) Presentation (7 results)

  • [Journal Article] Finiteness of Cousin cohomologies, Trans. Amer.2008

    • Author(s)
      川崎健
    • Journal Title

      Math. Soc. vol.360, no.5

      Pages: 2709-2739

    • Related Report
      2008 Final Research Report
  • [Journal Article] On Faltings' annihilator theorem, Proc. Amer.2008

    • Author(s)
      川崎健
    • Journal Title

      Math. Soc. vol.136, no.4

      Pages: 1205-1211

    • Related Report
      2008 Final Research Report
  • [Presentation] Buchsbaumness of graded modules associated to m-primary ideals in the equi-I-invariant case2007

    • Author(s)
      山岸規久道
    • Organizer
      The 3^<rd> Japan-Vietnam Joint Seminar on Commutative Algebra
    • Place of Presentation
      Hanoi, Vietnam
    • Year and Date
      2007-12-03
    • Related Report
      2008 Final Research Report
  • [Presentation] Buchsbaumness of graded modules associated tom-primary ideals in the equi-I-invariant case2007

    • Author(s)
      山岸 規久道
    • Organizer
      The 3rd Japan-Vietnam Joint Seminaron Commutative Algebra, Hanoi, December 3-7., 2007
    • Place of Presentation
      Institute of Mathematics,Vietnamese Academy of Science and Technology
    • Year and Date
      2007-12-03
    • Related Report
      2007 Annual Research Report
  • [Presentation] The Annihilator Theorem of Faltings with uniform property in the sense of Raghavan2006

    • Author(s)
      川崎健
    • Organizer
      Commutative Algebra and its Interactions with Algebraic Geometry
    • Place of Presentation
      Luminy/France
    • Year and Date
      2006-05-25
    • Related Report
      2008 Final Research Report
  • [Presentation] On Faltings' annihilator Theorem2006

    • Author(s)
      川崎健
    • Organizer
      The 2nd Japan-Vietnam Joint Seminar on Commutative Algebra
    • Place of Presentation
      明治大学生田校舎(川崎市)
    • Year and Date
      2006-03-24
    • Related Report
      2008 Final Research Report
  • [Presentation] Faltingsの零化域定理について2006

    • Author(s)
      川崎健
    • Organizer
      第18回可換環論セミナー
    • Place of Presentation
      北海道立道民活動センター かでる2・7(札幌市),
    • Year and Date
      2006-01-31
    • Related Report
      2008 Final Research Report
  • [Presentation] On Sally modules of m-primary ideals In Buchsbaum rings2005

    • Author(s)
      山岸規久道
    • Organizer
      第27回可換環論シンポジウム
    • Place of Presentation
      インテック大山研修センター
    • Year and Date
      2005-11-16
    • Related Report
      2008 Final Research Report
  • [Presentation] On Faltings' annihilator theorem2005

    • Author(s)
      川崎健
    • Organizer
      第27回可換環論シンポジウム
    • Place of Presentation
      インテック大山研修センター(富山市)
    • Year and Date
      2005-11-15
    • Related Report
      2008 Final Research Report

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Published: 2005-04-01   Modified: 2016-04-21  

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