Study of F-blowup and singularity

• Project/Area Number: 20840036
• Research Category: Grant-in-Aid for Young Scientists (Start-up)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Kagoshima University
• Principal Investigator: YASUDA Takehiko Kagoshima University, 大学院・理工学研究科(理学系), 准教授 (30507166)
• Project Period (FY): 2008 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥3,276,000 (Direct Cost: ¥2,520,000、Indirect Cost: ¥756,000); Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2008: ¥1,716,000 (Direct Cost: ¥1,320,000、Indirect Cost: ¥396,000)
• Keywords: 特異点 / 正標数 / フロベニウス射 / 非可交換代数幾何 / 代数幾何学 / F爆発

Research Abstract

In this research, I studied F-blowup and singularity, and obtained several results. Relations between two different subjects have been found out. Monotonicity of F-blowup sequence and F-pure singularity. Boundedness of F-blowup sequence and singularity of finite F-representation type. The F-blowup and the noncommutative algebraic geometry. Especially, the last one has offered a new direction to my research. Then I have introduced the noncommutative Frobenius morphism and applied it to noncommutative desingularization.

Research Products

• [Journal Article] Noncommutative resolution, F-blowups and D-modules (2009)
  • Author(s): Yukinobu Toda, Takehiko Yasuda
  • Journal Title: Advances in Mathematics 222 Pages: 318-330
  • Peer Reviewed
• [Journal Article] On monotonicity of F-blowup sequences (2009)
  • Author(s): Takehiko Yasuda
  • Journal Title: Illinois Journal of Mathematics 53 Pages: 101-110
  • Peer Reviewed
• [Journal Article] Flag higher Nash blowups (2009)
  • Author(s): Takehiko Yasuda
  • Journal Title: Communications in Algebra 37 Pages: 1001-1015
  • Peer Reviewed
• [Presentation] Frobenius morphisms and noncommutative resolutions (2010)
  • Author(s): Takehiko Yasuda
  • Organizer: Algebraic geometry in characteristic p and related topics
  • Place of Presentation: Tokyo
  • Year and Date: 2010-02-19
• [Presentation] Frobenius morphisms and noncommutative resolutions (2010)
  • Author(s): 安田健彦
  • Organizer: Algebraic geometry in characteristic p and related topics
  • Place of Presentation: 東京大学
  • Year and Date: 2010-02-19
• [Presentation] 非可換爆発におけるフロベニウス射の平坦性と大域次元の有限性 (2010)
  • Author(s): 安田健彦
  • Organizer: 複素幾何と代数幾何の若手研究集会
  • Place of Presentation: 熊本大学
  • Year and Date: 2010-02-18
• [Presentation] A standard noncommutative resolution of a toric singularity via differential operators (2010)
  • Author(s): 安田健彦
  • Organizer: 第5回代数・解析・幾何学セミナー
  • Place of Presentation: 鹿児島大学
  • Year and Date: 2010-02-16
• [Presentation] An application of the Frobenius morphism of a noncommutative blowup (2009)
  • Author(s): Takehiko Yasuda
  • Organizer: Higher Dimensional Algebraic Geometry
  • Place of Presentation: Kyoto, Japan
  • Year and Date: 2009-12-17
• [Presentation] An application of the Frobenius morphism of a noncommutative blowup (2009)
  • Author(s): 安田健彦
  • Organizer: Higher Dimensional Algebraic Geometry
  • Place of Presentation: 京都大学
  • Year and Date: 2009-12-17
• [Presentation] Noncommutative resolution and Frobenius morphism (2009)
  • Author(s): Takehiko Yasuda
  • Organizer: The 5th Franco-Japanese Symposium on Singularities
  • Place of Presentation: Strasbourg, France
  • Year and Date: 2009-08-27
• [Presentation] F-blowup (2009)
  • Author(s): 安田健彦
  • Organizer: Commutative Algebra Seminar
  • Place of Presentation: ミシガン大学
  • Year and Date: 2009-03-19
• [Presentation] Noncommutative resolution via Frobenius morphisms and D-modules (2008)
  • Author(s): 安田健彦
  • Organizer: 代数幾何学セミナー
  • Place of Presentation: 名古屋大学
  • Year and Date: 2008-11-17
• [Remarks]
  • URL: http://www.sci.kagoshima-u.ac.jp/~yasuda/