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On the Gorensteinness of Rees algebras

Research Project

Project/Area Number 19740001
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionHokkaido University of Education

Principal Investigator

IAI Shin-ichiro  Hokkaido University of Education, 教育学部, 准教授 (50333125)

Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥2,360,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥360,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2007: ¥800,000 (Direct Cost: ¥800,000)
KeywordsFLC環 / Gorenstein環 / Rees代数 / a standard system of parameters / blow-up代数 / 拡大Rees代数 / 正準加群 / Buchsbaum局所環 / a standard svstem of parameters / generalized Cohen-Macaulay環
Research Abstract

The purpose of this research is to investigate the Gorensteinness of Rees algebras over Noetherian local rings. The main problem can be stated as follows. "Is there an arithmetic Gorensteinfication in the case where the base ring has finite local cohomology?" In this research, we showed that a certain ideal of Kawasaki's arithmetic Macaulayfication gives the Gorenstein Rees algebra whenever the base ring is quasi-Gorenstein.

Report

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

    (8 results)

All 2009 2008 2007

All Presentation (8 results)

  • [Presentation] Gorenstein Rees algebras over rings of depth one having finite local cohomology2009

    • Author(s)
      居相真一郎
    • Organizer
      第31回可換環論シンポジウム
    • Place of Presentation
      大阪
    • Year and Date
      2009-11-26
    • Related Report
      2009 Final Research Report
  • [Presentation] Gorenstein Rees algebras over rings of depth one having finite local cohomology2009

    • Author(s)
      居相真一郎
    • 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
    • Year and Date
      2009-11-26
    • Related Report
      2009 Annual Research Report
  • [Presentation] Gorenstein Rees algebras over generalized Cohen-Macaulay rings of depth one2009

    • Author(s)
      Shin-ichiro Iai
    • Organizer
      The 4th Japan-Vietnam Joint Seminar on Commutative Algebra
    • Place of Presentation
      川崎
    • Year and Date
      2009-02-18
    • Related Report
      2009 Final Research Report
  • [Presentation] Gorenstein Rees algebras over generalized Cohen-Macaulay rings of depth one2009

    • Author(s)
      Shin-ichiro Iai
    • Organizer
      The 4^<th> Japan-Vietnam Joint Seminar on Commutative Algebra
    • Place of Presentation
      明治大学
    • Year and Date
      2009-02-18
    • Related Report
      2008 Annual Research Report
  • [Presentation] On Gorenstein Rees algebras2008

    • Author(s)
      Shin-ichiro Iai
    • Organizer
      International Conference on Commutative Algebra
    • Place of Presentation
      横浜
    • Year and Date
      2008-03-21
    • Related Report
      2009 Final Research Report 2007 Annual Research Report
  • [Presentation] On Gorenstein Rees algebras over rings with finite local cohomology2007

    • Author(s)
      Shin-ichiro Iai
    • Organizer
      The 3rd Japan-Vietnam Joint Seminar on Commutative Algebra
    • Place of Presentation
      ベトナム国
    • Year and Date
      2007-12-03
    • Related Report
      2009 Final Research Report 2007 Annual Research Report
  • [Presentation] The blowup algebras over rings with finite local cohomology2007

    • Author(s)
      居相真一郎
    • Organizer
      第29回可換環論シンポジウム
    • Place of Presentation
      名古屋
    • Year and Date
      2007-11-20
    • Related Report
      2009 Final Research Report
  • [Presentation] The blowup algebras over rings with Finite local cohomology2007

    • Author(s)
      居相 真一郎
    • Organizer
      第29回可換環論シンポジウム
    • Place of Presentation
      名古屋
    • Year and Date
      2007-11-20
    • Related Report
      2007 Annual Research Report

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

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