Study of Kahler Ricci flows
| Project/Area Number |
24540092
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Sophia University |
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Principal Investigator |
TSUJI Hajime 上智大学, 理工学部, 教授 (30172000)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| 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 / ケーラー多様体 / 極小モデル / フランス / パリ / 極値的体積形式 / 標準測度 / 半正値性 / 国際研究交流 / ケーラー・アインシュタイン計量 / 複素多様体 |
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| 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.
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Report
(4 results)
Research Products
(13 results)
