Study of generalized Kahler-Einstein metrics

2011 Fiscal Year Final Research Report

• 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
• Keywords: ケーラー多様 / アインシュタイン計量 / ベルグマン核

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 Pages: 1469-1501
  • DOI: DOI:10.1353/ajm.2011.0047
• [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] Global generation of relative pluricanonical systems
  • Author(s): Hajime TSUJI
  • Journal Title: arXiv math Volume: 1012 Pages: 0844
• [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
• [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] 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
• [Book] 複素多様体論
  • Author(s): 辻元
  • Publisher: サイエンス社(出版予定)