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On secant varieties of projective varieties

Research Project

Project/Area Number 19540055
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

KAJI Hajime  Waseda University, 理工学術院, 教授 (70194727)

Project Period (FY) 2007 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords代数幾何学 / 射影多様体 / 割線多様体 / ガウス写像 / 射影双対 / 再帰的 / 分離拡大 / セグレ積 / reflexivity / 双対多様体
Research Abstract

射影多様体の割線多様体を調べる際, 射影多様体のガウス写像や射影双対を調べることが重要と改めて気づき, 主に深澤知氏(日本学術振興会特別研究員, 受入機関 : 早稲田大学理工学術院)との共同研究を行った. そして, セグレ多様体の射影双対に関する再帰性, および, 与えられた代数多様体の射影モデルのガウス写像の階数について研究を行った. 当該研究期間中, 3本の論文を学術雑誌(どれも査読あり)に発表し, 国際会議等(2件)を含む8件の口頭発表を行った. また, 2008年度末の時点において, 掲載決定済みの論文が1本, 投稿中の論文が1本, 準備中の論文が1本ある.

Report

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

    (19 results)

All 2009 2008 2007 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (14 results)

  • [Journal Article] The reflexivity of a Segre product of projective varieties2008

    • Author(s)
      S. Fukasawa, H. Kaji
    • Journal Title

      Math. Annalen 342

      Pages: 279-289

    • Related Report
      2008 Annual Research Report 2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Existence of a non-reflexive embedding with birational Gauss map for a projective variety2008

    • Author(s)
      S. Fukasawa, H. Kaji
    • Journal Title

      Math. Nachrichten 281

      Pages: 1412-1417

    • Related Report
      2008 Annual Research Report 2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] The separability of the Gauss map and the reflexivity for a projective surface2007

    • Author(s)
      S. Fukasawa, H. Kaji
    • Journal Title

      Math. Zeitschrift 256

      Pages: 699-703

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] The separability of the Gauss map and the reflexivity for a projective surface2007

    • Author(s)
      S.Fukasawa, H.Kaji
    • Journal Title

      Math.Zeitschrift 256

      Pages: 699-703

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence of a nonreflexive embedding with birational Gauss map for a projective variety

    • Author(s)
      S.Fukasawa, H.Kaji
    • Journal Title

      Math.Nachrichten (掲載決定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] The separability of the Gauss map versus the reflexivity2009

    • Author(s)
      楫元
    • Organizer
      研究集会「代数幾何学in九州」
    • Place of Presentation
      九州大学
    • Year and Date
      2009-02-02
    • Related Report
      2008 Final Research Report
  • [Presentation] The separability of the Gauss map versus the reflexivity2009

    • Author(s)
      楫 元
    • Organizer
      研究集会「代数幾何学 in 九州」
    • Place of Presentation
      九州大学
    • Year and Date
      2009-02-02
    • Related Report
      2008 Annual Research Report
  • [Presentation] The reflexivity of a Segre product of projective varieties2008

    • Author(s)
      楫元, 深澤知
    • Organizer
      日本数学会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-25
    • Related Report
      2008 Annual Research Report 2008 Final Research Report
  • [Presentation] Existence of a non-reflexive embedding with birational Gauss map for a projective variety2008

    • Author(s)
      楫元, 深澤知
    • Organizer
      日本数学会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-25
    • Related Report
      2008 Annual Research Report 2008 Final Research Report
  • [Presentation] Existence of a nonreflexive embedding with birational Gauss map for a projective variety2007

    • Author(s)
      楫元
    • Organizer
      International Conference "IV Iberoamerican Conference on Complex Geometry"
    • Place of Presentation
      Ouro Preto, Brazil
    • Year and Date
      2007-08-17
    • Related Report
      2008 Final Research Report
  • [Presentation] Existence of a nonreflexive embedding with birational Gauss map for a projective variety2007

    • Author(s)
      H.Kaji
    • Organizer
      International Conference"IV Iberoamerican Conference on Complex Geometry"
    • Place of Presentation
      Ouro Preto,Brazil
    • Year and Date
      2007-08-17
    • Related Report
      2007 Annual Research Report
  • [Presentation] Existence of a nonreflexive embedding with birational Gauss map for a projective variety2007

    • Author(s)
      楫元
    • Organizer
      Seminario de Algebra "Sun from Japan", Instituto Nacional de Matematica Pura e Aplicada
    • Place of Presentation
      Rio de Janeiro, Brazil
    • Year and Date
      2007-08-10
    • Related Report
      2008 Final Research Report
  • [Presentation] Existence of a nonreflexive embedding with birational Gauss map for a projective variety2007

    • Author(s)
      H.Kaji
    • Organizer
      Seminario de Algebra "Sun from Japan"
    • Place of Presentation
      IMPA,Brazil
    • Year and Date
      2007-08-10
    • Related Report
      2007 Annual Research Report
  • [Presentation] Projective varieties with degenerate secant varieties2007

    • Author(s)
      楫元
    • Organizer
      Colloquium, National Institute for Mathematical Sciences
    • Place of Presentation
      Daejeon, Korea
    • Year and Date
      2007-06-14
    • Related Report
      2008 Final Research Report
  • [Presentation] Projective varieties with degenerate secant varieties2007

    • Author(s)
      H.Kaji
    • Organizer
      Colloquium, National Institute for Mathematical Sciences
    • Place of Presentation
      Daejeon,Korea
    • Year and Date
      2007-06-14
    • Related Report
      2007 Annual Research Report
  • [Presentation] Projective varieties with degenerate secant varieties2007

    • Author(s)
      楫元
    • Organizer
      Algebraic Geometry Seminar, Seoul National University
    • Place of Presentation
      Seoul, Korea
    • Year and Date
      2007-06-12
    • Related Report
      2008 Final Research Report
  • [Presentation] Projective geometry of adjoint varieties2007

    • Author(s)
      楫元
    • Organizer
      Algebraic Geometry Seminar, Seoul National University
    • Place of Presentation
      Seoul, Korea
    • Year and Date
      2007-06-12
    • Related Report
      2008 Final Research Report
  • [Presentation] Projective geometry of adjoint varieties2007

    • Author(s)
      H.Kaji
    • Organizer
      Algebraic Geometry Seminar, Seoul National University
    • Place of Presentation
      Seoul,Korea
    • Year and Date
      2007-06-12
    • Related Report
      2007 Annual Research Report
  • [Presentation] Projective varieties with degenerate secant varieties2007

    • Author(s)
      H.Kaji
    • Organizer
      Algebraic Geometry Seminar, Seoul National University
    • Place of Presentation
      Seoul,Korea
    • Year and Date
      2007-06-12
    • Related Report
      2007 Annual Research Report

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

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