Stability of direct images by Frobenius morphisms and algebraic geometry in positive characteristic

• Project/Area Number: 20840032
• Research Category: Grant-in-Aid for Young Scientists (Start-up)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Hiroshima University
• Principal Investigator: KITADAI Yukinori Hiroshima University, 工学研究科, 特任助教 (30511563)
• 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: ベクトル束 / 安定性 / 半安定ベクトル束 / 正標数 / フロベニウス写像 / de Rham複体 / 小平消滅定理 / 代数幾何学 / 平安定余接束 / dc Rham 複体 / de Rham 複体

Research Abstract

We studied the problem of whether taking direct images of semistable vector bundles on algebraic varieties in positive characteristic by Frobenius morphisms preserves semistability or not and related problems. Calculations to find concrete examples of algebraic surfaces whose cotangent bundles are semitable or are not semistable by Frobenius pullback several times were proceeded.

Research Products

• [Presentation] Canonical filtrations and stability of direct images by Frobenius morphisms over surfaces (2009)
  • Author(s): 北臺如法
  • Organizer: Informal presentations in the atrium
  • Place of Presentation: Mathematical Sciences Research Institute (米国バークリー)
  • Year and Date: 2009-02-09
• [Presentation] 余接束のフロベニウス写像による直像の安定性 (2008)
  • Author(s): 北臺如法
  • Organizer: 早大理工代数幾何学セミナー
  • Place of Presentation: 早稲田大学大久保キャンパス51号館18階08室
  • Year and Date: 2008-11-28
• [Presentation] Stability of direct images of cotangent bundles by Frobenius morphisms (2008)
  • Author(s): 北臺如法
  • Organizer: Algebraic Geometry in positive characteristics and related topics
  • Place of Presentation: 名古屋大学大学院多元数理科学研究科
  • Year and Date: 2008-11-07
• [Presentation] 余接束のフロベニウス写像による直像の安定性 (2008)
  • Author(s): 北臺如法
  • Organizer: 東北大学代数幾何セミナー
  • Place of Presentation: 東北大学理学部
  • Year and Date: 2008-05-09
• [Presentation] フロベニウス写像による直像の安定性と正標数代数幾何(1)-(3) (2008)
  • Author(s): 北臺如法
  • Organizer: 代数幾何学都留ワークショップ2008
  • Place of Presentation: 都留文科大学