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A study on compactifications of complex affine planes and spaces

Research Project

Project/Area Number 22540051
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

FURUSHIMA Mikio  熊本大学, 大学院・自然科学研究科, 教授 (00165482)

Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords代数幾何学 / コンパクト化 / 端末特異点 / ファノ空間 / アフィン平面 / アフィン空間 / ファノ多様体
Research Abstract

(1) Research 1: The boundary of compactification of C^2 into Hirzebruch surfacesconsists of two irreducible components, one of which can have a singularity byL.Brenton. Then I can construct more general examples including the Brenton’ s one. Ialso prove that one of the irreducible components of boundary divisor is a smoothrationa curve. Further , I suggested the possibility of a birational geometric proof of thetheorem by Abyankar-Moh- Suzuki. (2) Research 2: I studied the detail structure of singular Fano threefolds withGorenstein terminal singularities as a compactification of C^2.,especially , applying thetheory of smoothing of Fano threefolds with Gorenstein terminal singularities, I candetermine the detail structure of the known examples of singular Fanocompactifications of C^3..

Report

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

    (13 results)

All 2013 2012 2011

All Journal Article (3 results) (of which Peer Reviewed: 3 results) Presentation (10 results) (of which Invited: 1 results)

  • [Journal Article] Hirzebruchsurfaces and compactifications of C^22013

    • Author(s)
      古島幹雄,石田明男
    • Journal Title

      The Proceedings of the Conference on Affine Algebraic Geometry

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Hirzebruch surfaces and compactifications of C^ 22013

    • Author(s)
      古島幹雄
    • Journal Title

      The Proceedings of the Conference on Affine Algebraic Geometry,Osaka

      Volume: 1 Pages: 42-51

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Hirzebruch surfaces and compactifications of C^22012

    • Author(s)
      Mikio Furushima
    • Journal Title

      The Proceedings of the Conference on Affine Algebraic Geometry, Osaka, March 2011

      Volume: (掲載確定)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Presentation] C^3 の非射影的コンパクト化について2012

    • Author(s)
      古島幹雄
    • Organizer
      南九州第数系集会
    • Place of Presentation
      熊本大学黒髪キャンパス (熊本)
    • Year and Date
      2012-08-30
    • Related Report
      2012 Final Research Report
  • [Presentation] Compactifications of C^32012

    • Author(s)
      古島幹雄
    • Organizer
      高次元代数多様体とベクトル束の代数幾何学
    • Place of Presentation
      高次元代数多様体とベクトル束の代数幾何学
    • Year and Date
      2012-03-17
    • Related Report
      2012 Final Research Report
  • [Presentation] Compactifications of C^32012

    • Author(s)
      古島幹雄
    • Organizer
      高次元代数多様体とベクトル束の代数幾何学研究集会
    • Place of Presentation
      九州大学(福岡県)(招待講演)
    • Year and Date
      2012-03-17
    • Related Report
      2011 Annual Research Report
  • [Presentation] C^ 3の非射影的コンパクト化について2012

    • Author(s)
      古島幹雄
    • Organizer
      南九州代数系集会
    • Place of Presentation
      熊本大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Hiezebruch 曲面と C^2のコンパクト化2011

    • Author(s)
      古島幹雄
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      信州大学(松本)
    • Year and Date
      2011-10-01
    • Related Report
      2012 Final Research Report
  • [Presentation] フェルマー3次曲面についての一注意2011

    • Author(s)
      古島幹雄,大嶋康裕
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      信州大学(松本)
    • Year and Date
      2011-10-01
    • Related Report
      2012 Final Research Report
  • [Presentation] Hirzebruch曲面とC^2のコンパクト化2011

    • Author(s)
      古島幹雄
    • Organizer
      日本数学秋季総合分科会
    • Place of Presentation
      信州大学(長野県)
    • Year and Date
      2011-10-01
    • Related Report
      2011 Annual Research Report
  • [Presentation] フェルマー3次曲面についての一注意2011

    • Author(s)
      古島幹雄
    • Organizer
      日本数学秋季総合分科会
    • Place of Presentation
      信州大学(長野県)
    • Year and Date
      2011-10-01
    • Related Report
      2011 Annual Research Report
  • [Presentation] Hirzebruchsurfaces and compactifications of C^22011

    • Author(s)
      古島幹雄,石田明男
    • Organizer
      第7回アフィン代数幾何学研究集会
    • Place of Presentation
      関西学院大学大阪梅田キャンパス(大阪)
    • Year and Date
      2011-03-06
    • Related Report
      2012 Final Research Report
  • [Presentation] On the compactifications of C^2 and the Hirzebruch surfaces2011

    • Author(s)
      古島幹雄
    • Organizer
      Conference on Affine Algebraic Geometry
    • Place of Presentation
      関西学院大学(大阪梅田キャンパス)
    • Year and Date
      2011-03-06
    • Related Report
      2010 Annual Research Report

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

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