Aspects of purely inseparable morphisms in algebraic geometry

• Project/Area Number: 22540039
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Tohoku University
• Principal Investigator: HARA Nobuo 東北大学, 大学院・理学研究科, 准教授 (90298167)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 代数幾何 / 代数多様体 / 特異点 / 正標数 / フロベニウス写像 / F爆発 / 純非分離射 / F-特異点 / F-爆発 / F-サンドイッチ / 単純楕円型特異点 / フロベニウス射 / F正則 / Fサンドイッチ / 平坦化

Research Abstract

We studied Frobenius sandwich singularities and F-blowups of2-dimensional singularities, which are closely related to purely inseparable morphisms in algebraic geometry in positive characteristic. We obtained results on the following subjects: (1) Frobenius sandwich surface singularities whose F-blowup is not the minimal resolution; (2) F-blowups of F-regular surface singularities; (3) F-blowups of non-F-regular rational double points; (4) F-blowups of simple elliptic singularities. (1), (3) and (4) are due to joint works with Tadakazu Sawada and Takehiko Yasuda.

Research Products

• [Journal Article] F- blowups of normal surface singular- ities (2013)
  • Author(s): N. Hara, T. Sawada and T. Yasuda
  • Journal Title: Algebra & Number Theory Volume: (印刷中)
  • Peer Reviewed
• [Journal Article] F-blowups of F-regular surface Singularities, Proc (2012)
  • Author(s): N. Hara
  • Journal Title: Amer. Math. Soc Volume: 140 Pages: 2215-2226
  • URL: http://dx.doi.org/10.1090/S0002-9939-2011-11074-8
  • Peer Reviewed
• [Journal Article] F-bolowups of F-regular surface singularities (2012)
  • Author(s): N. Hara
  • Journal Title: Proc. Amer. Math. Soc. Volume: 140 Pages: 2215-2216
  • Peer Reviewed
• [Journal Article] F-blowups of F-regular surfiace singularities (2012)
  • Author(s): N.Hara
  • Journal Title: Proc.Amer.Math.Soc. Volume: (未定)(掲載確定)
  • Peer Reviewed
• [Journal Article] Splitting of Frobenius sandwiches (2011)
  • Author(s): N. Hara and T. Sawada
  • Journal Title: in Higher dimensional Algebraic Geometry (editors: S. Mukai and N. Nakayama), RIMS kokyuroku Bessatsu Volume: B24 Pages: 121-141
  • Peer Reviewed
• [Journal Article] Splitting of Frobenius sandwiches (2011)
  • Author(s): N.Hara, T.Sawada
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: B24 Pages: 121-141
  • Peer Reviewed
• [Journal Article] Splitting of Frobenius sandwiches
  • Author(s): N.Hara, T.Sawada
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: (未定)(掲載確定)
  • Peer Reviewed
• [Journal Article] F-blowups of F-regular surface singularities
  • Author(s): N.Hara
  • Journal Title: Proc.Amer.Math.Soc. Volume: (未定)(掲載確定)
  • Peer Reviewed
• [Presentation] フロベニウス直像とF爆発に関する幾つかの問題 (2013)
  • Author(s): 原伸生
  • Organizer: 杜の都代数幾何学研究集会
  • Place of Presentation: 東北大学
  • Year and Date: 2013-02-14
• [Presentation] Structure of the F-blowups of simple elliptic singularities (2012)
  • Author(s): 原伸生
  • Organizer: RIMS 研 究集会「高次元双有理幾何の周辺」
  • Place of Presentation: 京都大学
  • Year and Date: 2012-06-12
• [Presentation] Aspects of F-regularity-old and new- (2011)
  • Author(s): 原伸生
  • Organizer: 代数学シンポジウム
  • Place of Presentation: 岡山大学
  • Year and Date: 2011-08-09
• [Presentation] Aspects of F-regularity-old and new (2011)
  • Author(s): 原伸生
  • Organizer: 代数学シンポジウム
  • Place of Presentation: 岡山大学
  • Year and Date: 2011-08-09
• [Presentation] F-blowups of normal surface Singularities (2011)
  • Author(s): N. Hara
  • Organizer: Workshop on Algebraic Geometry in Positive Characteristic
  • Place of Presentation: KIAS, 韓国
  • Year and Date: 2011-05-26
• [Presentation] F-blowups of normal surface singularities (2011)
  • Author(s): N.Hara
  • Organizer: Workshop on Algebraic Geometry in Positive Characteristic
  • Place of Presentation: 韓国高等研究所(KIAS),韓国
  • Year and Date: 2011-05-26
• [Presentation] F-blowups of F-regular surface singularities (2011)
  • Author(s): 原伸生
  • Organizer: 日本数学会
  • Place of Presentation: 早稲田大学
  • Year and Date: 2011-03-23
• [Presentation] F-blowups of F-regular surface singularities (2011)
  • Author(s): 原伸生
  • Organizer: 代数幾何学研究集会-ファノ多様体と正標数上の話題を中心として-
  • Place of Presentation: 九州大学
  • Year and Date: 2011-02-21
• [Presentation] F-blowups of F-regular surface Singularities (2011)
  • Author(s): 原伸生
  • Organizer: 研究集会「ファノ多様体 と正標数の話題を中心として」
  • Place of Presentation: 九州大学
  • Year and Date: 2011-02-11
• [Presentation] F-blowups of F-regular surface singularities (2011)
  • Author(s): 原伸生
  • Organizer: 日本数学会年会
  • Place of Presentation: 早稲田大学(アブストラクト原稿の み)
• [Presentation] F-blowups of certain Frobenius sandwich singularities and rational double points (2010)
  • Author(s): N. Hara
  • Organizer: Fudan-Tohoku Joint Workshop on Algebraic Geometry
  • Place of Presentation: 復旦大学,中国
  • Year and Date: 2010-06-01
• [Presentation] F-blowups of certain Frobenius sandwich singularities and rational double points (2010)
  • Author(s): N.Hara
  • Organizer: Fudan-Tohoku joint workshop on algebraic geometry
  • Place of Presentation: 復旦大学、上海,中国
  • Year and Date: 2010-06-01
• [Presentation] Structure of the F-blowups of simple elliptic singularities
  • Author(s): 原 伸生
  • Organizer: RIMS研究集会『高次元代数幾何の周辺』
  • Place of Presentation: 京都大学
• [Presentation] フロベニウス直像とF爆発に関する幾つかの問題
  • Author(s): 原 伸生
  • Organizer: 杜の都代数幾何学研究集会
  • Place of Presentation: 東北大学