2003 Fiscal Year Final Research Report Summary
The Hitchin-Kobayashi correspondence for Manifolds
| Project/Area Number |
13440023
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Osaka University |
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Principal Investigator |
MABUTCHI Toshiki Osaka University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (80116102)
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| Co-Investigator(Kenkyū-buntansha) |
KOMATSU Gen KOMATSU,Gen, 大学院・理学研究科, 助教授 (60108446)
FUJIWARA Akio FUJIWARA,Akio, 大学院・理学研究科, 助教授 (30251359)
SUKUMA Makoto SUKUMA,Makoto, 大学院・理学研究科, 助教授 (30178602)
YAMATO Kenji YAMATO,Kenji, 大学院・理学研究科, 助教授 (70093474)
ENOKI Ichiro ENOKI,Ichiro, 大学院・理学研究科, 助教授 (20146806)
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| Project Period (FY) |
2001 – 2003
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| Keywords | Hitchin-Kobayashi correspondence / Stability / Kahler-Einstein metric / Extremal Kahler metric / constant scalar curvature / Zhang's critical matric / Chow metric / Asymptotic Bergman Kernel |
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| Research Abstract |
Recently, Donaldson established the stability of a projective algebraic Kahler manifold M of constant scalar curvature essentially when the connected linear algebraic part G(M) of the group of holomorphic automorphisms of M is selnisimple.
By generalizing the concept of stability to the case where G(M) is not semisimple, we extend Donaldson's result to extremal Kahler cases even when G(M) is not semisimple. Namely, we showed that a polarized projective algebraic manifold with an extremal Kahler metric in polarization class is always stable in this generalized sense. This in particular implies that an extremal Kahler metric in a fixed integral Kahler class on a projective algebraic manifold M is unique, if any, modulo the action of G(M).
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