Birational geometry of higher-dimensional algebraic varieties higher-dimensional algebraic

• 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 京都大学, 大学院・理学研究科, 准教授 (60324711)
• Project Period (FY): 2008 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥12,480,000 (Direct Cost: ¥9,600,000、Indirect Cost: ¥2,880,000); Fiscal Year 2011: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000); Fiscal Year 2010: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2009: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2008: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
• Keywords: 極小モデル / 消滅定理 / アバンダンス予想 / 標準束公式 / トーリック幾何学 / 混合ホッジ構造 / 代数曲面論 / 対数的標準特異点 / 半安定退化 / 劣随伴公式 / 双有理幾何 / トーリック幾何 / フリップ / トーリック多様体

Research Abstract

I mainly studied the birational geometry of higher-dimensional algebraic varieties. I obtained various vanishing theorems by using the theory of mixed Hodge structures. By these new vanishing theorems, I established the fundamental theorems of the minimal model theory for log canonical pairs. I also studied the abundance conjecture, isolated log canonical singularities, variations of mixed Hodge structure, and so on. In addition to the above mentioned studies, I am interested in the toric geometry, singular algebraic surfaces, generalizations of Kodaira's canonical bundle formula, and so on.

Research Products

• [Journal Article] Fundamental theorems for the log minimal model program (2011)
  • Author(s): Osamu Fujino
  • Journal Title: Publ. Res. Inst. Math. Sci Volume: Sci. 47
  • NAID: 110008606193
• [Journal Article] On isolated log canonical sigularities with index one (2011)
  • Author(s): Osamu Fujino
  • Journal Title: Math. Sci. Univ Volume: 18 Pages: 299-323
• [Journal Article] Semi-stable minimal model program for varieties with trivial canonical divisor (2011)
  • Author(s): Osamu Fujino
  • Journal Title: Proc. Japan Acad. Ser. A Math. Sci Volume: Sci. 87
  • NAID: 40018844394
• [Journal Article] Non-vanishing theorem for log canonical pairs (2011)
  • Author(s): Osamu Fujino
  • Journal Title: J. Algebraic Geom Volume: 41, no.4 Pages: 771-783
  • NAID: 120005593587
• [Journal Article] Fundamental theorems for the log minimal model program (2011)
  • Author(s): Osamu Fujino
  • Journal Title: Publ.Res.Inst.Math.Sci. Volume: 47 Pages: 727-789
  • NAID: 110008606193
  • Peer Reviewed
• [Journal Article] Non-vanishing theorem for log canonical pairs (2011)
  • Author(s): Osamu Fujino
  • Journal Title: J.Algebraic Geom. Volume: 20 Pages: 771-783
  • NAID: 120005593587
  • Peer Reviewed
• [Journal Article] Semi-stable minimal model program for varieties with trivial canonical divisor (2011)
  • Author(s): Osamu Fujino
  • Journal Title: Proc.Japan Acad.Ser.A Math.Sci. Volume: 87 Pages: 25-30
  • NAID: 40018844394
  • Peer Reviewed
• [Journal Article] Finite generation of the log canonical ring in dimension four (2010)
  • Author(s): Osamu Fujino
  • Journal Title: Kyoto Journal of Mathematics Volume: Vol.50, No.4 Pages: 671-684
  • NAID: 120005593588
• [Journal Article] Introduction to the theory of quasi-log varieties (2010)
  • Author(s): Osamu Fujino
  • Journal Title: Classification of Algebraic varieties Pages: 289-303
• [Journal Article] On Kawamata's theorem Classification of Algebraic varieties (2010)
  • Author(s): Osamu Fujino, On Kawamata. s theorem
  • Journal Title: Classification of Algebraic varieties Pages: 305-315
• [Journal Article] Theory of non-lc ideal sheaves : basic properties (2010)
  • Author(s): Osamu Fujino
  • Journal Title: Kyoto Journal of Mathematics Volume: Vol.50, No.2 Pages: 225-245
• [Journal Article] Effective base point free theorem for log canonical pairs II (2010)
  • Author(s): Osamu Fujino
  • Journal Title: Angehrn-Siu type theorems Volume: 59 Pages: 303-312
• [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
  • NAID: 120005593588
  • 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] Theory of non-lc ideal sheaves : basic properties (2010)
  • Author(s): Osamu Fujino
  • Journal Title: Kyoto J.Math. Volume: 50 Pages: 225-245
  • Peer Reviewed
• [Journal Article] Effective base point free theorem for log canonical pairs, II.Angehrn-Siu type theorems (2010)
  • Author(s): Osamu Fujino
  • Journal Title: Michigan Math.J. Volume: 59 Pages: 303-312
  • Peer Reviewed
• [Journal Article] Finite generation of the log canonical ring in dimension four (2010)
  • Author(s): Osamu Fujino
  • Journal Title: Kyoto J.Math. Volume: 50 Pages: 671-684
  • NAID: 120005593588
  • 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 Volume: 61 Pages: 475-481
• [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
  • NAID: 40016807003
  • 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
  • NAID: 130004558892
  • 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] 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 Pages: 95-100
  • NAID: 40016807003
  • Peer Reviewed
• [Journal Article] Smooth projective toric varieties whose nontrivial nef line bundles are big (2009)
  • Author(s): Osamu Fujino, Hiroshi Sato
  • Journal Title: Proc.Japan Acad.Ser.A Math.Sci. 85 Pages: 89-94
  • NAID: 40016671765
  • 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 Pages: 162-184
  • NAID: 130004558892
  • 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. 61 Pages: 475-481
  • Peer Reviewed
• [Journal Article] Three-dimensional terminal toric flips (2009)
  • Author(s): Osamu Fulino, 他3名
  • Journal Title: Cent. Eur. J. Math. 7(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
  • NAID: 110006870105
  • Peer Reviewed
• [Journal Article] Vanishing theorems for toric polyhedra (2008)
  • Author(s): Osamu Fujino
  • Journal Title: RIMS Kokyuroku Bessatsu 9 Pages: 81-95
  • Peer Reviewed
• [Presentation] Minimal model theory for log surfaces (2011)
  • Author(s): 藤野修
  • Organizer: 東大数理;代数幾何学セミナー
  • Place of Presentation: 東京大学数理科学研究科(招待講演)
  • Year and Date: 2011-10-31
• [Presentation] On isolated log canonical singularities with index one (2011)
  • Author(s): Osamu Fujino
  • Organizer: 特異点論とそのひろがり
  • Place of Presentation: 京都大学
  • Year and Date: 2011-08-22
• [Presentation] Fundamental theorems for the logminimal model program (2011)
  • Author(s): Osamu Fujino
  • Organizer: Analytic aspects of complex algebraic geometry
  • Place of Presentation: フランス
  • Year and Date: 2011-02-15
• [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] Fundamental theorems for the log minimal model program (2011)
  • Author(s): Osamu Fujino
  • Organizer: Analytic aspects of complex algebraic geometry
  • Place of Presentation: CIRM(アメリカ)(招待講演)
  • Year and Date: 2011-02-15
• [Presentation] Vanishing theorems and their applications (2011)
  • Author(s): Osamu Fujino
  • Organizer: Miniworkshop of Algebra
  • Place of Presentation: 台湾大学
• [Presentation] Vanishing theorems and their applications (2011)
  • Author(s): Osamu Fujino
  • Organizer: Miniworkshop of Algebra
  • Place of Presentation: 台湾大学(招待講演)
• [Presentation] Minimalmodel theory for log surfaces (2010)
  • Author(s): Osamu Fujino
  • Organizer: Workshop Birational Geometry
  • Place of Presentation: ICMS,エディンバラ
  • Year and Date: 2010-12-10
• [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] 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(イギリス)(招待講演)
  • 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] 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] Logminimal model program I, II, III,アバンダンス予想の代数 (2009)
  • Author(s): Osamu Fujino
  • Organizer: 解析的両面からの研究
  • Place of Presentation: 京都大学
  • Year and Date: 2009-09-14
• [Presentation] Introduction to the log minimal modelprogram (2009)
  • Author(s): Osamu Fujino
  • Organizer: WorkshoponComplex Geometry
  • Place of Presentation: Korean Institute for Advanced Study
  • Year and Date: 2009-09-10
• [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): Osamu Fujino
  • Organizer: International Conference of Mathematics
  • Place of Presentation: National Taiwan University台湾
  • Year and Date: 2009-07-07
• [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 and torsion-free theorems for algebraic varieties (2009)
  • Author(s): Osamu Fujino
  • Organizer: International Conference of Mathematics
  • Place of Presentation: National Taiwan University (台湾)
  • 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] 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
• [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] Vanishing and torsion-free theorems for the log minimal model program (2008)
  • Author(s): Osamu Fujino
  • Organizer: Algebraic Geometry Seminar
  • Place of Presentation: Princeton University
  • 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: 日本数学会秋季総合分科会特別講演
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-09-25
• [Presentation] 極小モデル理論 (2008)
  • Author(s): 藤野修
  • Organizer: 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: 2008-09-25
• [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
• [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
• [Presentation] 消滅定理と単射性定理(3日連続講演) (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
• [Presentation] Vanishing theorem and non-vanishing theorem for log canonical pairs (2007)
  • Author(s): Osamu Fujino
  • 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: 2007-07-02
• [Remarks]
  • URL: http://www.math.kyoto-u.ac.jp/.fujino/