2013 Fiscal Year Final Research Report
Destabilizing objects and multiplier ideal sheaves
| Project/Area Number |
23654023
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | The University of Tokyo (2012-2013)
Tokyo Institute of Technology (2011) |
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Principal Investigator |
FUTAKI Akito 東京大学, 数理(科)学研究科(研究院), 教授 (90143247)
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| Project Period (FY) |
2011 – 2013
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| Keywords | アインシュタイン計量 / ケーラー多様体 / K-安定性 / 乗数イデアル層 / リッチ・ソリトン |
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| Research Abstract |
The multiplier ideal sheaves appear when the Monge-Ampere equation can not be solved. On the other hand the Futaki invariant is an obstruction to the existence of Kahler-Einstein metrics, and the existence of Kahler-Einstein metrics is reduced to solving the Monge-Ampere equation. It is therefore expected to have some relationship between the multiplier ideal sheaves and the Futaki invariant. Yuji Sano and I obtained results in this direction. As a similar research in the same context, Yuji Sano and I obtained a universal lower bound of the diameter of compact shrinking Ricci solitons, which are the self-similar solutions to the Ricci flow. This lower bound was further improved in a joint work with Hai-Zhong Li and Xiang-Dong Li.
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