2007 Fiscal Year Final Research Report Summary
Constant scalar curvature Kaehler metrics and the stabilty of polarized algebraic manifolds in the geometric invariant theory
Project/Area Number |
17540069
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Geometry
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Research Institution | Kanazawa University |
Principal Investigator |
NAKAGAWA Yasuhiro Kanazawa University, School of Mathematics & Physics, Associate Professor (90250662)
|
Project Period (FY) |
2005 – 2007
|
Keywords | Einstein-Kaehler metrics / Geometric Invariant Thory / Stablity / Futaki characters / Kaehler-Ricci solitons |
Research Abstract |
We have studied the conjecture which states that the stability of polarized algebraic manifolds in the geometric invariant theory is equivalent to the existence of constant scalar curvature Kaehler metrics on that manifolds, namely "Kobayashi-Hitchin correspondence for polarized algebraic manifolds". In particular, we observed Kaehler-Ricci solitons, which are an generalization of Einstein-Kaehler metrics, from the view points of K-energy, which plays an important role in the research of Einstein-Kaehler metrics, and we could generalize Kaehler-Ricci solitons to the case of general Kaehler classes. Moreover, we have studied the constraction of non-trival examples of this generalized Kaehler-Ricci solitons. Then, we could prove the existence of generalized Kaehler-Ricci solitons for the Kaehler classes, for which the volume of fibers is sufficiently small compare to that of O-section, on the compactification of the holomorphic line bundle over the complex projective line.
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Research Products
(6 results)