Birational geometry for higher dimensional algebraic varieties

2010 Fiscal Year Self-evaluation Report

• Project/Area Number: 20684001
• Research Category: Grant-in-Aid for Young Scientists (A)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Kyoto University
• Principal Investigator: FUJINO Osamu Kyoto University, 大学院・理学研究科, 准教授 (60324711)
• Project Period (FY): 2008 – 2011
• Keywords: 極小モデル / 消滅定理 / アバンダンス予想

Research Abstract

高次元代数多様体の双有理幾何学の研究を推進する。複素射影代数多様体の双有理分類は代数幾何学の最も基本的な問題の一つである。私は極小モデル理論の立場からこの問題に取り組んでいる。

Research Products

• [Journal Article] Finite generation of the log canonical ring in dimension four (2010)
  • Author(s): Osamu Fujino
  • Journal Title: Kyoto J.Math. 50, no.4 Pages: 671-685
  • Peer Reviewed
• [Journal Article] Theory of non-lc ideal sheaves : basic properties (2010)
  • Author(s): Osamu Fujino
  • Journal Title: Kyoto J.Math. 50, no.2 Pages: 225-245
  • Peer Reviewed
• [Journal Article] Effective base point free theorem for log canonical pairs, II. (2009)
  • Author(s): Osamu Fujino
  • Journal Title: Angehrn-Siu type theorems, Michigan Math.J. 59, no.2 Pages: 303-312
  • Peer Reviewed
• [Journal Article] Effective base point free theorem for log canonical pairs--Kollar type theorem (2009)
  • Author(s): Osamu Fujino
  • Journal Title: Tohoku Math.J. (2)61, no.4 Pages: 475-481
  • Peer Reviewed
• [Journal Article] On injectivity, vanishing and torsion-free theorems for algebraic varieties (2009)
  • Author(s): Osamu Fujino
  • Journal Title: Proc.Japan.Acad.Ser.A Math.Sci. 85, no.8 Pages: 95-100
  • Peer Reviewed
• [Journal Article] 極小モデル理論の新展開 (2009)
  • Author(s): 藤野修
  • Journal Title: 数学 61, no.2 Pages: 162-186
  • Peer Reviewed
• [Journal Article] Hiroshi Sato, Smooth projective toric varieties whose nontrivial nef line bundles are big (2009)
  • Author(s): Osamu Fujino
  • Journal Title: Proc.Japan Acad.Ser.A Math.Sci. 85, no.7 Pages: 89-94
  • Peer Reviewed
• [Journal Article] Three-dimensional terminal toric flips (2009)
  • Author(s): Osamu Fujino, Hiroshi Sato, Yukishige Takano, Hokuto Uehara
  • Journal Title: Cent.Eur.J.Math. 7, no.1 Pages: 46-53
  • Peer Reviewed
• [Journal Article] Vanishing theorems for toric polyhedra, Higher dimensional algebraic varieties and vector bundles (2008)
  • Author(s): Osamu Fujino
  • Journal Title: RIMS KoKyuroku Bessatsu, B9, Res.Inst.Math.Sci.(RIMS) Kyoto Pages: 81-95
  • Peer Reviewed
• [Presentation] Vanishing theorems and their applications (2011)
  • Author(s): Osamu Fujino
  • Organizer: Miniworkshop of Algebra
  • Place of Presentation: 台湾大学
  • Year and Date: 20110111-12
• [Presentation] Fundamental theorems for the log minimal model program (2011)
  • Author(s): 藤野修
  • Organizer: Analytic aspects of complex algebraic geometry
  • Place of Presentation: フランスCIRM
  • Year and Date: 2011-02-15
• [Presentation] Minimal model theory for log surfaces (2010)
  • Author(s): 藤野修
  • Organizer: Workshop birational geometry in honor of Slava Shokurov's 60th birthday
  • Place of Presentation: エディンバラ大学
  • Year and Date: 2010-12-10
• [Presentation] 代数多様体に対する消滅定理 (2010)
  • Author(s): 藤野修
  • Organizer: 京都大学談話会
  • Place of Presentation: 京都大学
  • Year and Date: 2010-04-21
• [Presentation] Log minimal model program I, II, III (2009)
  • Author(s): 藤野修
  • Organizer: アバンダンス予想の代数、解析両面からの研究
  • Place of Presentation: 京都大学数学教室
  • Year and Date: 20090914-20090915
• [Presentation] Vanishing theorems for algebraic varieties (2009)
  • Author(s): Osamu Fujino
  • Organizer: Invariants in Algebraic Geometry
  • Place of Presentation: 東京大学
  • Year and Date: 2009-11-09
• [Presentation] Introduction to the log minimal model program (2009)
  • Author(s): 藤野修
  • Organizer: Workshop on Complex Geometry
  • Place of Presentation: Korea Institute for Advanced Study
  • Year and Date: 2009-09-10
• [Presentation] Vanishing and torsion-free theorems for algebraic varieties (2009)
  • Author(s): 藤野修
  • Organizer: International Conference of Mathematics
  • Place of Presentation: 台湾大学
  • Year and Date: 2009-07-07
• [Presentation] Vanishing theorem and non-vanishing theorem for log canonical pairs (2009)
  • Author(s): 藤野修
  • Organizer: Hodge理論と代数幾何学
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2009-07-02
• [Presentation] 消滅定理と単射性定理 (2008)
  • Author(s): 藤野修
  • Organizer: Bergman核と代数幾何への応用
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 20080604-20080606
• [Presentation] Vanishing and torsion-free theorems for the log minimal model program (2008)
  • Author(s): 藤野修
  • Organizer: Algebraic Geometry Seminar
  • Place of Presentation: プリンストン大学
  • Year and Date: 2008-11-11
• [Presentation] 極小モデル理論と消滅定理 (2008)
  • Author(s): 藤野修
  • Organizer: 日本数学会 秋期総合分科会
  • Place of Presentation: 東京工業大学(特別講演)
  • Year and Date: 2008-09-25
• [Presentation] 極小モデル理論 (2008)
  • Author(s): 藤野修
  • Organizer: 名古屋大学大学院多元数理科学研究科、大談話会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2008-07-09