Projective Algebraic Geometry in Positive Characteristic

2012 Fiscal Year Final Research Report

• Project/Area Number: 22540055
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Waseda 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
• Keywords: ガウス写像 / 射影双対 / 再帰性 / 正標数

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.”

Research Products

• [Journal Article] Cubic hypersurfaces admitting an embedding with Gauss map of rank 0 (2012)
  • Author(s): K.Furukawa
  • Journal Title: Advances in Mathematics Volume: 230 Pages: 1174-1183
  • 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
  • Peer Reviewed
• [Presentation] A tangential trisecant lemma (2012)
  • 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
• [Presentation] A tangential trisecant lemma (2012)
  • 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
• [Presentation] A tangential trisecant lemma (2012)
  • 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
• [Presentation] Gauss maps in positive characteristic (2010)
  • 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
• [Remarks]
  • URL: http://pc193097.pc.waseda.ac.jp/