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Deformation of isolated singularities from the viewpoint of computational algebraic analysis

Research Project

Project/Area Number 19740077
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Basic analysis
Research InstitutionKinki University

Principal Investigator

NAKAMURA Yayoi  Kinki University, 理工学部, 講師 (60388494)

Project Period (FY) 2007 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥2,690,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2008: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2007: ¥1,000,000 (Direct Cost: ¥1,000,000)
Keywords代数解析 / D加群 / 代数的局所コホモロジー / 孤立特異点 / グロタンディック双対性
Research Abstract

本研究では、特異点にデフォーメーションを施した際の代数的局所コホモロジーの変化を解析することにより、特異点の性質を研究した.擬斉次孤立特異点に関して、ミルナー代数の単項基底に注目したデフォーメーションを行った場合の代数的局所コホモロジーの変化の解析を行った.また、デフォーメーションによるコホモロジーの重みのジャンプ幅と特異点のb-関数との対応を解析することにより、b-関数の変化とモダリティーのとの間に成り立つ関係を得た.

Report

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

    (9 results)

All 2009 2008 2007 Other

All Journal Article (4 results) (of which Peer Reviewed: 4 results) Presentation (4 results) Remarks (1 results)

  • [Journal Article] Annihilating ideals for an algebraic local cohomology class2009

    • Author(s)
      S. Tajima and Y. Nakamura
    • Journal Title

      Journal of Symbolic Computation 44

      Pages: 435-448

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Annihilating ideals for an algebraic local cohomology class2009

    • Author(s)
      S. Tajima, Y. Nakamura
    • Journal Title

      Journal of Symbolic Computation 44

      Pages: 435-448

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On invariants of Reiffen's isolated singularity2008

    • Author(s)
      Y. Nakamura
    • Journal Title

      RIMS Kokyuroku Bessatsu B5

      Pages: 7-14

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On invariants of Reiffen's isolated singularity2008

    • Author(s)
      中村弥生
    • Journal Title

      RIMS Kokyuroku Bessatsu B5

      Pages: 7-14

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] An invariant of Reiffen's isolated singularity2008

    • Author(s)
      中村弥生
    • Organizer
      Geometry and Analysis on Complex Algebraic Varieties
    • Place of Presentation
      モスクワ独立大学(ロシア)
    • Year and Date
      2008-09-22
    • Related Report
      2008 Final Research Report
  • [Presentation] An invariant of Reiffen's isolated singularity2008

    • Author(s)
      中村弥生
    • Organizer
      Geometry and Analysis on Complex Algebraic Varieties
    • Place of Presentation
      モスクワ独立大学(モスクワ)
    • Year and Date
      2008-09-22
    • Related Report
      2008 Annual Research Report
  • [Presentation] A computation of homological index of a vector field on an isolated complete intersection singularity2007

    • Author(s)
      中村弥生
    • Organizer
      Geometry and Analysis on Complex Algebraic Varieties
    • Place of Presentation
      東京農工大学
    • Year and Date
      2007-11-23
    • Related Report
      2008 Final Research Report
  • [Presentation] A Computation of homological index of a vector field on an isolated complete intersection singularity.2007

    • Author(s)
      中村弥生
    • Organizer
      Geometry and Analysis on Complex Algebraic Varieties
    • Place of Presentation
      東京農工大
    • Year and Date
      2007-11-23
    • Related Report
      2007 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.kindai.ac.jp/~yayoi/

    • Related Report
      2008 Final Research Report

URL: 

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

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