Deformation of isolated singularities from the viewpoint of computational algebraic analysis

• Project/Area Number: 19740077
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Kinki 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: ¥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.

Research Products

• [Journal Article] Annihilating ideals for an algebraic local cohomology class (2009)
  • Author(s): S. Tajima and Y. Nakamura
  • Journal Title: Journal of Symbolic Computation 44 Pages: 435-448
  • Peer Reviewed
• [Journal Article] Annihilating ideals for an algebraic local cohomology class (2009)
  • Author(s): S. Tajima, Y. Nakamura
  • Journal Title: Journal of Symbolic Computation 44 Pages: 435-448
  • Peer Reviewed
• [Journal Article] On invariants of Reiffen's isolated singularity (2008)
  • Author(s): Y. Nakamura
  • Journal Title: RIMS Kokyuroku Bessatsu B5 Pages: 7-14
  • Peer Reviewed
• [Journal Article] On invariants of Reiffen's isolated singularity (2008)
  • Author(s): 中村弥生
  • Journal Title: RIMS Kokyuroku Bessatsu B5 Pages: 7-14
  • Peer Reviewed
• [Presentation] An invariant of Reiffen's isolated singularity (2008)
  • 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
• [Presentation] An invariant of Reiffen's isolated singularity (2008)
  • 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
• [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: 東京農工大学
  • Year and Date: 2007-11-23
• [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
• [Remarks]
  • URL: http://www.math.kindai.ac.jp/~yayoi/