Study of generalized Kahler-Einstein metrics

• Project/Area Number: 21540093
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Sophia University
• Principal Investigator: TSUJI Hajime 上智大学, 理工学部, 教授 (30172000)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: ケーラー多様 / アインシュタイン計量 / ベルグマン核 / ケーラー計量 / リッチ曲率 / 標準束 / 小平次元 / 多重劣調和関数 / 射影多様体 / モンジュ・アンペール方程式 / リッチ流 / モンジューアンペール方程式 / 多重標準系 / ケーラー多様体 / 標準測度

Research Abstract

I have proved that the logarithmic plurisubharmonicity of the canonical measure on a smooth projective family of nonnegative Kodaira dimension and the smooth dependence of the canonical measure on the family. As an application, we have proven the global generation of the direct image of the pluricanonical systems. This result gives the affirmative answer to Iitaka's conjecture. The proof uses the Monge-Ampere foliation.

Research Products

• [Journal Article] Canonical singular hermitian metrics on relative canonical bundles (2011)
  • Author(s): Hajime TSUJI
  • Journal Title: American Jour. of Math Volume: 133 Issue: 6 Pages: 1469-1501
  • DOI: 10.1353/ajm.2011.0047
  • Peer Reviewed
• [Journal Article] Some conjectures and problems in complex geometry (2011)
  • Author(s): Hajime TSUJI
  • Journal Title: 数理解析研究所講究録 Volume: 1731 Pages: 137-150
• [Journal Article] Dynamical construction of Kahler-Einstein metrics (2010)
  • Author(s): Hajime TSUJI
  • Journal Title: Nagoya Math. J Volume: 199 Pages: 107-122
• [Journal Article] Dynamical construction of K\"ahler-Einstein metrics (2010)
  • Author(s): Hajime TSUJI
  • Journal Title: Nagoya Math.J. Volume: 199 Pages: 107-122
  • Peer Reviewed
• [Journal Article] Dynamical construction of Kaehler-Einstein metrics (2010)
  • Author(s): Hajime Tsuji
  • Journal Title: Nagoya Math.Journal 119(To appear(掲載確定))
  • Peer Reviewed
• [Journal Article] Local semipositivity of relative canonical bundles (2010)
  • Author(s): Hajime Tsuji
  • Journal Title: RIMS kokyuroku (未定, To appear(掲載確定))
• [Journal Article] Global generation of relative pluricanonical systems
  • Author(s): Hajime TSUJI
  • Journal Title: arXiv math Volume: 1012 Pages: 844-844
• [Journal Article] Ricci iterations and canonical singular Kahler-Einstein currents on LC paris
  • Author(s): Hajime TSUJI
  • Journal Title: arXiv math Volume: 0904 Pages: 5445-5445
• [Journal Article] Semipositivity of Kahler-Ricci flows
  • Author(s): Hajime Tsuji
  • Journal Title: RIMS kokyuroku 2012appear
• [Presentation] Semipositivity of Kahler-Ricci flows (2012)
  • Author(s): 辻元
  • Organizer: 日本数学会春季総合分科会
  • Place of Presentation: 東京理科大学
  • Year and Date: 2012-03-27
• [Presentation] Parmeter dependence of singular Kahler-Einstein metrics (2012)
  • Author(s): 辻元
  • Place of Presentation: 大阪大学
  • Year and Date: 2012-03-17
• [Presentation] Semipositivity of twisted Kahler-Einstein metrics (2012)
  • Author(s): 辻元
  • Organizer: Special Seminar, Institute Fourier
  • Place of Presentation: フランス
  • Year and Date: 2012-03-04
• [Presentation] フランス (2011)
  • Author(s): 辻元
  • Organizer: 数理研研究集会ベルグマン核とその周辺
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2011-09-06
• [Presentation] Semipositivity of Kahler-Ricci flows (2011)
  • Author(s): 辻元
  • Organizer: 数理研研究集会ベルグマン核とその周辺
  • Place of Presentation: 京都大学数理解析研究所(招待講演)
  • Year and Date: 2011-09-06
• [Presentation] Variation of canonical measures on a smooth projective families (2011)
  • Author(s): 辻元
  • Organizer: Differential Geomery and Complex Geometry, Leminy
  • Place of Presentation: マルセイユ、フランス
  • Year and Date: 2011-03-19
• [Presentation] Canonical volume form on compact Kahler manifolds (2010)
  • Author(s): 辻元
  • Organizer: Shokurov Conference
  • Place of Presentation: エジンバラ、イギリス
  • Year and Date: 2010-12-11
• [Presentation] On the variation of canoial volume form on smooth projective families (2010)
  • Author(s): 辻元
  • Organizer: 複素幾何菅平シンポジウム
  • Place of Presentation: 長野県真田町菅平
  • Year and Date: 2010-10-26
• [Presentation] Canonical measures and semipositivity of relative canonical bundles (2009)
  • Author(s): Hajime Tsuji
  • Organizer: Extremal Kaehler metrics
  • Place of Presentation: Banff., Canada
  • Year and Date: 2009-06-09
• [Book] 複素多様体論
  • Author(s): 辻元
  • Publisher: サイエンス社(出版予定)