2005 Fiscal Year Final Research Report Summary
Geometric Non-linear problems and stability in invariant theory
| Project/Area Number |
14204002
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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 | Tokyo Institute of Technology |
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Principal Investigator |
FUTAKI Akito Tokyo Institute of Technology, Department of Mathematics, Professor, 大学院・理工学研究科, 教授 (90143247)
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| Co-Investigator(Kenkyū-buntansha) |
ITOH Mitsuhiro Tsukuba University, Institute of Mathematics, Professor, 大学院・数理物質科学研究科, 教授 (40015912)
MABICHI Toshiki Osaka University, Department of Mathematics, Professor, 大学院・理学研究科, 教授 (80116102)
NAKAJIMA Hiraku Kyoto University, Department of Mathematics, Professor, 大学院・理学研究科, 教授 (00201666)
LI Wein Kyushu University, Department of Mathematics, Assisrant Professor, 大学院・数理科学研究院, 助教授 (60304002)
TSUJI Hajime Sophia University, Department of Mathematics, Professor, 理工学部, 教授 (30172000)
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| Project Period (FY) |
2002 – 2005
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| Keywords | scalar curvature / K-stability / geometric invariant theory / moment map |
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| Research Abstract |
The purpose of this research is to find a necessary and sufficient condition for the existence of Kaehler metrics of constant scalar curvature in terms of stability in geometric invariant theory. There is a description of stability expressed using moment maps on symplectic manifolds. Namely orbits having a zero of the moment map are the stable orbits. From this view point it is important to study the space of all complex structures compatible with a given symplectic form, which is an infinite dimensional symplectic manifold and of which the scalar curvature is the moment map. I developed a perturbation theory of this fact and studied the infinite dimensional symplectic manifold from perturbed structures. Secondly T.Mabuchi proved that asymptotic Chow stability is equivalent to asymptotic Hilbert scheme stability.
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