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Classification of isolated singularities by means of algebraic geometric studies of invariants

Research Project

Project/Area Number 18540051
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionNihon University

Principal Investigator

TOMARI Masataka  Nihon University, 文理学部, 教授 (60183878)

Co-Investigator(Kenkyū-buntansha) WATANABE Keiichi  日本大学, 文理学部, 教授 (10087083)
MATSUURA Yutaka  日本大学, 文理学部, 准教授 (50096905)
Project Period (FY) 2006 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥3,630,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥630,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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: ¥900,000 (Direct Cost: ¥900,000)
Keywords代数幾何学 / 特異点 / ゴレンスタイン性 / 有理特異点 / 基本サイクル / 極大イデアルサイクル / ブロウイングアップ / 2次元星型特異点 / 重複度 / F-threshold / 単純K3特異点 / 非退化完全交差式 / 中心フィルトレーション / F-thresholds / 重複度予想 / 超曲面特異点 / simple K3特異点 / ニュートン境界 / フィルター付きブロウイングアップ / 幾何種数 / フロベニウス写像 / 特異点解消 / 代数的スタック / ベロネーゼ環 / 字数付き環 / exceptional log canonical singularity / 密着閉包 / stack
Research Abstract

Tomari found a sufficient condition for the new 5 classes of hypersurface simple K3 singularities would be the last of 95+5 classes. The four of these 5 classes are the classical one found in the Ishii-Tomari theory on Veronese subring of famous 95 classes, but the other one is completely new one. Watanabe has been studying F-threshold, integral closures, and tight closures of several ideals and got many results.

Report

(6 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report   Self-evaluation Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (21 results)

All 2010 2009 2008 2007 2006 Other

All Journal Article (12 results) (of which Peer Reviewed: 6 results) Presentation (9 results)

  • [Journal Article] Multigraded rings, Diagonal subalgebras and rational singularities2009

    • Author(s)
      K. Kurano, E. Sato, A. Singh, K.-i. Watanabe
    • Journal Title

      J. of Algebra 322

      Pages: 3248-3267

    • Related Report
      2009 Final Research Report
  • [Journal Article] Multigraded rings, diagonal subalgebras and rational singularities2009

    • Author(s)
      K.Kurano, E.Sato, A.Singh, K.-i.Watanabe
    • Journal Title

      J.of Algebra 322

      Pages: 3248-3267

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] F-thresholds, tight closure, integral closure, and multiplicity bounds2008

    • Author(s)
      C. Huneke, M. Mustata, S. Takagi, K.W atanabe
    • Journal Title

      Michigan Math. J. vol.57

      Pages: 463-483

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] F-thresholds, tight closure, integral closure, and multiplicity bounds2008

    • Author(s)
      C. Huneke, M. Mustata, S. Takagi, K. Watanabe
    • Journal Title

      Michigan Math. J. 57

      Pages: 463-483

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] F-thresholds, tight closure, integral closure, and multiplicity bounds2007

    • Author(s)
      K. i. Watanabe, C. Huneke, M. Mustata, S. Takagi
    • Journal Title

      Michigan Math. J. vol.57

      Pages: 60-67

    • Related Report
      2009 Final Research Report
  • [Journal Article] Totally reflexive modules constructed from smooth projective curves of genus g geq 22007

    • Author(s)
      K. i. Watanabe, R. Takahashi
    • Journal Title

      Archiv der Mathematik 89

      Pages: 60-67

    • Related Report
      2009 Final Research Report
  • [Journal Article] Totally reflexive modules constructed from smooth projective curves of genus g \geq 22007

    • Author(s)
      K. i. Watanabe, R. Takahashi
    • Journal Title

      Archiv der Mathematik 89

      Pages: 60-67

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Adjacent integrally closed ideals in 2-dimensional regular local rings.2006

    • Author(s)
      S. Noh, K.-i. Watanabe
    • Journal Title

      J. of Algebra 300

      Pages: 156-166

    • Related Report
      2009 Final Research Report
  • [Journal Article] Adjacent integrally closed ideals in 2-dimensional regular local rings.2006

    • Author(s)
      S.Noh, K, -i.Watanabe
    • Journal Title

      J. of Algebra 300

      Pages: 156-166

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Coefficient ideal of ideals generated by monomials

    • Author(s)
      S.Ohnihsi, K.-i.Watanabe
    • Journal Title

      Communications in Algebra (掲載決定, 巻号未定)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] F-thresholds, tight closure, integral closure, and multiplicity bounds

    • Author(s)
      K. i. Watanabe, C. Huneke, M. Mustata, S. Takagi
    • Journal Title

      Michigan Math. J. (未定)(掲載決定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Totally reflexive modules constructed from smooth projective curves of genus g≧2

    • Author(s)
      R.Takahashi, K.-i.Watanabe
    • Journal Title

      Arkiv fur Math. (to appear 巻、号、発行年、ページ数未定)

    • Related Report
      2006 Annual Research Report
  • [Presentation] 2次元正規特異点のmaximal ideal cycleとfundamental cycleについて2010

    • Author(s)
      泊昌孝
    • Organizer
      研究集会「特異点山形セミナー2010」
    • Place of Presentation
      山形大学
    • Year and Date
      2010-03-03
    • Related Report
      2009 Final Research Report
  • [Presentation] 2次元正規特異点の maximal ideal cycle と fundamental cycle について2010

    • Author(s)
      泊昌孝
    • Organizer
      研究集会「特異点山形セミナー2010」
    • Place of Presentation
      山形大学
    • Year and Date
      2010-03-03
    • Related Report
      2009 Annual Research Report
  • [Presentation] Classification of hypersurface simple K3 singularities 95 and others2009

    • Author(s)
      泊昌孝
    • Organizer
      研究集会「代数幾何in九州」
    • Place of Presentation
      九州大学箱崎キャンパス
    • Year and Date
      2009-02-02
    • Related Report
      2009 Final Research Report
  • [Presentation] classification of hypersurface simple K3 singularities- 95 and others2009

    • Author(s)
      泊 昌孝
    • Organizer
      研究集会「代数幾何 in 九州」
    • Place of Presentation
      九州大学箱崎キャンパス
    • Year and Date
      2009-02-02
    • Related Report
      2008 Annual Research Report
  • [Presentation] Classification of hypersurface simple K3 singularities-95 and others2007

    • Author(s)
      泊昌孝
    • Organizer
      埼玉大学理学部, 日本数学会
    • Year and Date
      2007-03-27
    • Related Report
      2009 Final Research Report
  • [Presentation] Classification of hypersurface simple K3 singularities-95 and others2007

    • Author(s)
      泊昌孝
    • Organizer
      日本数学会
    • Place of Presentation
      埼玉大学理学部
    • Year and Date
      2007-03-27
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] Methods of Characteristic p>0 in Singularity Theory" Summer School.2007

    • Author(s)
      K. i. Watanabe
    • Organizer
      Characteristic p methods in Algebraic Geometry
    • Place of Presentation
      Drobeta-Turum-Severin; Romania
    • Related Report
      2009 Final Research Report
  • [Presentation] Methods of characteristic p>0 in Singularity Theory2007

    • Author(s)
      K. i. Watanabe
    • Organizer
      Summer School."Characteristic p methods in Algebraic Geometry"
    • Place of Presentation
      Drobeta-Turum-Severin; Romania
    • Related Report
      2007 Annual Research Report
  • [Presentation] On F-thresholds、京都大学数理研短期共同研究2006

    • Author(s)
      渡辺敬一
    • Organizer
      京都大学数理研
    • Related Report
      2009 Final Research Report

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Published: 2006-04-01   Modified: 2016-04-21  

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