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The structures of hypersurface simple K3 singularities

Research Project

Project/Area Number 22540060
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

KATANAGA Atsuko  信州大学, 全学教育機構, 講師 (20373128)

Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywords特異点論 / 超曲面孤立特異点 / 単純K3特異点 / リンク / K3曲面 / トポロジー / オ-リック予想 / 特性多項式 / ザリスキ予想 / 特異点 / オーリック予想 / 正規K3曲面
Research Abstract

We show the existence of infinitely many links of non-degenerate simple K3 singularities defined by non-quasi-homogeneous polynomials, which do not appear in the case of the singularities defined by quasi-homogeneous polynomials. Moreover, we give a result that relates the diffeomorphism types of the links of non-degenerate semi-quasi-homogeneous hypersurface simple K3 singularities with the singularities of the normal K3 surface that appears as the exceptional divisor of the resolution of the singularity. We also classify links of the some complex 3-dimensional hypersurface isolated singularities up to regular homotopies under some conditions.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (17 results)

All 2013 2012 2011 2010 Other

All Journal Article (2 results) (of which Peer Reviewed: 2 results) Presentation (15 results)

  • [Journal Article] The links specific to hypersurface simple K3 singularities2013

    • Author(s)
      Atsuko Katanaga
    • Journal Title

      The proceeding of the 6th Franco-Japanese Symposium on singularities

      Volume: -

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The links specific to hypersurface simple K3 singularities

    • Author(s)
      Atsuko Katanaga
    • Journal Title

      The proceeding of the 6th Franco-Japanese Symposium on singularities

      Volume: (掲載確定)

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Presentation] Links of singularities up to regular homotopy2013

    • Author(s)
      片長敦子
    • Organizer
      特異点セミナー
    • Place of Presentation
      東京理科大学
    • Year and Date
      2013-03-12
    • Related Report
      2012 Final Research Report
  • [Presentation] Null Sasakian links in dimension 52012

    • Author(s)
      片長敦子
    • Organizer
      信州トポロジーセミナー
    • Place of Presentation
      信州大学
    • Year and Date
      2012-07-11
    • Related Report
      2012 Final Research Report
  • [Presentation] The topology of hypersurface simple K3 singularities2012

    • Author(s)
      片長敦子
    • Organizer
      特異点論と幾何構造
    • Place of Presentation
      長野市生涯学習センター
    • Year and Date
      2012-06-01
    • Related Report
      2012 Final Research Report
  • [Presentation] The resolutions of hypersurface simple K3 singularities2012

    • Author(s)
      片長敦子(共同発表:島田伊知朗)
    • Organizer
      Branched Coverings,Degenerations,and Related Topics 2012
    • Place of Presentation
      Graduate School of Advanced Sciences of Matter, Hiroshima University
    • Year and Date
      2012-03-08
    • Related Report
      2012 Final Research Report
  • [Presentation] The resolutions of hypersurface simple K3 singularities2012

    • Author(s)
      片長敦子(共同発表:島田伊知朗)
    • Organizer
      Branched Coverings、 Degenerations、and Related Topics 2012
    • Place of Presentation
      Graduate School of Advanced Sciences of Matter、Hiroshima University(招待講演)
    • Year and Date
      2012-03-08
    • Related Report
      2011 Annual Research Report
  • [Presentation] The links specific to hypersurface simple K3 singularities2011

    • Author(s)
      片長敦子
    • Organizer
      国際シンポジウム「Singularities in Geometry and Topology -The 6th Franco-Japanese Symposium on Singularities-」(招待講演)
    • Place of Presentation
      The Nishijin Plaza,Lecture Hall, Kyushu University
    • Year and Date
      2011-09-06
    • Related Report
      2012 Final Research Report
  • [Presentation] The links specific to hypersurface simple K3 singularities2011

    • Author(s)
      片長敦子
    • Organizer
      国際シンポジウム「Singularities in Geometry and Topology-The 6th Franco-Japanese Symposium on Singularities-
    • Place of Presentation
      The Nishijin Plaza Lecture Hall、Kyushu University(招待講演)
    • Year and Date
      2011-09-06
    • Related Report
      2011 Annual Research Report
  • [Presentation] The missing numbers related to hypersurface simple K3 Singularities2011

    • Author(s)
      片長敦子
    • Organizer
      Seminar Geometrie(招待講演)
    • Place of Presentation
      Mathematisches Institut Universitat Basel
    • Year and Date
      2011-05-06
    • Related Report
      2012 Final Research Report
  • [Presentation] The missing numbers related to hypersurface simple K3 Singularities2011

    • Author(s)
      片長敦子
    • Organizer
      Seminar Geometrie
    • Place of Presentation
      Mathematisches Institut、Universitat Basel(招待講演)
    • Year and Date
      2011-05-06
    • Related Report
      2011 Annual Research Report
  • [Presentation] The numbers associated withthe links of hypersurface simple K3 Singularities2010

    • Author(s)
      片長敦子
    • Organizer
      談話会
    • Place of Presentation
      信州大学理学部
    • Year and Date
      2010-11-16
    • Related Report
      2012 Final Research Report
  • [Presentation] The numbers associated with the links of hypersurface simple K3 singularities2010

    • Author(s)
      片長敦子
    • Organizer
      談話会
    • Place of Presentation
      信州大学理学部
    • Year and Date
      2010-11-16
    • Related Report
      2010 Annual Research Report
  • [Presentation] The links of simple K3 singularities defined by specific non-quasi-homogeneous polynomials2010

    • Author(s)
      片長敦子
    • Organizer
      研究集会「特異点と多様体の幾何学」
    • Place of Presentation
      山形大学理学部
    • Year and Date
      2010-09-17
    • Related Report
      2012 Final Research Report 2010 Annual Research Report
  • [Presentation] The topology of hypersurface simple K3 singularities

    • Author(s)
      片長 敦子
    • Organizer
      特異点論と幾何構造
    • Place of Presentation
      長野市生涯学習センター
    • Related Report
      2012 Annual Research Report
  • [Presentation] Null Sasakian links in dimension 5

    • Author(s)
      片長 敦子
    • Organizer
      信州トポロジーセミナー
    • Place of Presentation
      信州大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] Links of singularities up to regular homotopy

    • Author(s)
      片長 敦子
    • Organizer
      特異点セミナー
    • Place of Presentation
      東京理科大学
    • Related Report
      2012 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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