2013 Fiscal Year Final Research Report
AdS/CFT correspondence and GIT stablity
| Project/Area Number |
21244003
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | The University of Tokyo (2012-2013)
Tokyo Institute of Technology (2009-2011) |
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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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| Co-Investigator(Kenkyū-buntansha) |
YASUI Yukinori 大阪市立大学, 大学院理学研究科, 准教授 (30191117)
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| Co-Investigator(Renkei-kenkyūsha) |
MABUCHI Toshiki 大阪大学, 大学院理学研究科, 教授 (80116102)
AKUTAGAWA Kazuo 東京工業大学, 大学院理工学研究科, 教授 (80192920)
ONO Kaoru 京都大学, 数理解析研究所, 教授 (20204232)
NAKAJIMA Hiraku 京都大学, 数理解析研究所, 教授 (00201666)
ONO Hajime 埼玉大学, 大学院理工学研究科, 准教授 (70467033)
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Keywords | アインシュタイン計量 / ケーラー多様体 / 佐々木多様体 / Fano多様体 / 平均曲率流 / リッチ・ソリトン / 自己相似解 |
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| Research Abstract |
A general existence result of toric Sasaki-Einstein metrics was established. As its application, an eternal solution of Kaehler Ricci flow was constructed on the canonical line bundle of toric Fano Manifolds.
On polarized manifolds with non-discrete automorphisms, it is shown that there are integral invariants which obstruct asymptotic Chow semi-stability. Using them it is possible to show the existence of a toric Fano Kaehler-Einstein manifold which is asymptotically unstable. It has been shown by S.K.Donaldson that a polarized manifolds with constant scalar curvature and with discrete automorphisms is asymptotically Chow-stable.
A universal lower diameter bound for compact shrinking Ricci solitons was obtained.
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