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Projective Algebraic Geometry in Positive Characteristic

Research Project

Project/Area Number 22540055
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  早稲田大学, 理工学術院, 教授 (70194727)

Co-Investigator(Renkei-kenkyūsha) FUKASAWA Satoru  山形大学, 理学部, 准教授 (20569496)
FURUKAWA Katsuhisa  早稲田大学, 理工学術院, 助教 (40648664)
Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywordsガウス写像 / 射影双対 / 再帰性 / 正標数 / 射影代数幾何
Research Abstract

I obtained a few results on non-singular projective varieties with Gauss map of rank zero, on the linearity of Gauss fibres, and on the linear degeneration of tangentially degenerate curves. I also organized a symposium “Miyako no Seihoku Algebraic Geometry Symposium.”

Report

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

    (14 results)

All 2012 2011 2010 Other

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

  • [Journal Article] Cubic hypersurfaces admitting an embedding with Gauss map of rank 02012

    • Author(s)
      K.Furukawa
    • Journal Title

      Advances in Mathematics

      Volume: 230 Pages: 1174-1183

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Projective varieties admitting an embedding with Gauss map of rank zero (with S. Fukasawa, K. Furukawa)2010

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

      Advances in Mathematics

      Volume: 224 Pages: 2645-2661

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Projective varieties admitting an embedding with Gauss map of rank zero2010

    • Author(s)
      楫元, 深澤知、古川勝久
    • Journal Title

      Advances in Mathematics

      Volume: 224 Pages: 2645-2661

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] A tangential trisecant lemma2012

    • Author(s)
      楫元
    • Organizer
      ALGA-2012 (the 12th Meeting of the Brazilian Group in Commutative Algebra and Algebraic Geometry)
    • Place of Presentation
      Instituto de Matematica Pura e Aplicada (リオデジャネイロ, ブラジル)
    • Year and Date
      2012-08-16
    • Related Report
      2012 Final Research Report
  • [Presentation] A tangential trisecant lemma2012

    • Author(s)
      楫元
    • Organizer
      高次元代数多様体とベクトル束の代数幾何学
    • Place of Presentation
      九州大学
    • Year and Date
      2012-03-16
    • Related Report
      2012 Final Research Report
  • [Presentation] A tangential trisecant lemma2012

    • Author(s)
      楫元
    • Organizer
      研究集会「高次元代数多様体とベクトル束の代数幾何学」
    • Place of Presentation
      九州大学(福岡)(招待講演)
    • Year and Date
      2012-03-16
    • Related Report
      2011 Annual Research Report
  • [Presentation] A tangential trisecant lemma2012

    • Author(s)
      楫元
    • Organizer
      Symposium on Projective Algebraic Varieties and Moduli
    • Place of Presentation
      Novotel Ambassador (釜山, 韓国)
    • Year and Date
      2012-02-13
    • Related Report
      2012 Final Research Report
  • [Presentation] A tangential trisecant lemma2012

    • Author(s)
      楫元
    • Organizer
      Symposium on Projective Algebraic Varieties and Moduli
    • Place of Presentation
      Novotel Ambassador(釜山,韓国)(招待講演)
    • Year and Date
      2012-02-13
    • Related Report
      2011 Annual Research Report
  • [Presentation] A tangential trisecant lemma2012

    • Author(s)
      楫 元
    • Organizer
      第12回代数幾何学可換代数 研究集会 (ALGA)
    • Place of Presentation
      ブラジル,リオデジャネイロ
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Homogeneous projective varieties with unique secant property2011

    • Author(s)
      楫元
    • Organizer
      大垣研究集会「シンプレクティック幾何学とその周辺」
    • Place of Presentation
      岐阜経済大学(岐阜)(招待講演)
    • Year and Date
      2011-11-09
    • Related Report
      2011 Annual Research Report
  • [Presentation] Gauss maps in positive characteristic2010

    • Author(s)
      楫元
    • Organizer
      Algebra Seminar
    • Place of Presentation
      ソウル国立大学(ソウル,韓国)(招待講演)
    • Year and Date
      2010-09-01
    • Related Report
      2010 Annual Research Report
  • [Presentation] Gauss maps in positive characteristic2010

    • Author(s)
      楫元
    • Organizer
      ALGA-2010 (the 10th Meeting of the Brazilian Group in Commutative Algebra and Algebraic Geometry)
    • Place of Presentation
      Instituto de Matematica Pura e Aplicada (リオデジャネイロ, ブラジル)
    • Year and Date
      2010-07-09
    • Related Report
      2012 Final Research Report
  • [Presentation] Gauss maps in positive characteristic2010

    • Author(s)
      楫元
    • Organizer
      ALGA-2010, the Tenth Meeting of the Brazilian Group in Commutative Algebra and Algebraic Geometry
    • Place of Presentation
      IMPA (Rio de Janeiro, Brazil)(招待講演)
    • Year and Date
      2010-07-09
    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://pc193097.pc.waseda.ac.jp/

    • Related Report
      2012 Final Research Report

URL: 

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

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