Study of Kahler Ricci flows

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540092
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• 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): 2012-04-01 – 2015-03-31
• Keywords: ケーラー・リッチ流 / ベルグマン核 / 随伴直線束 / 多重劣調和関数

Outline of Final Research Achievements

We study the family of fiberwise Kaehler-Ricci flows on a smooth projective family of projective varieties with pseudoeffective canonical classes. We have proven that if the initial form is a Kaehler form on the total space, the resulting family of Kahler-Ricci flows preserves the semipositivity. The method is the approximation of the Kaehler-Ricci flows in terms of the dynamical system of Bergman kernels and then apply the logarithmic plurisubharmonic variation properties of Bergman kernels due to B. Berndtsson. This resul can be viewed as a refinement of the semiposity of the direct image of pluri adjoint line bundles.

This reserch is a joint project with S. Boucksom in Ecole Polytechnic in Paris.

Free Research Field

複素多様体論