2010 Fiscal Year Final Research Report
Canonical Sasaki metrics and AdS/CFT correspondence
| Project/Area Number |
20740032
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
ONO Hajime Tokyo University of Science, 理工学部, 講師 (70467033)
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| Project Period (FY) |
2008 – 2010
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| Keywords | チャウ安定性 / ケーラー・アインシュタイン多様体 / 佐々木多様体 / ヒルベルト級数 |
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| Research Abstract |
In this project, we investigated geometric invariant theoretic (GIT) stability and relations between the existence of canonical Kahler metrics and GIT stability of polarized toric manifolds. Then we proved the following three results : (1) The derivative of Hilbert series has the same information with the family of integral invariants, which is an obstruction for asymptotic Chow semistability defined by Futaki. (2) We found the first example of an asymptotically Chow unstable Kahler-Einstein manifold. (3) We gave a combinatorial necessary condition for Chow semistability.
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