Scalar Curvature and Projective Embeddings, I
Scalar Curvature and Projective Embeddings, I
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DOI：
10.4310/jdg/1090349449
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发表时间：
2001-11
影响因子：
2.5
通讯作者：
S. Donaldson
中科院分区：
文献类型：
--
作者：
S. Donaldson
证明了极化Kahler流形上的常数量曲率度量是由特定的射影嵌入序列导出的度量的极限;满足H.罗作为推论，这给出了在给定的有理上同调类中常数量曲率Kahler度量的唯一性。证明使用的结果在文献中的伯格曼内核的渐近性。的参数提出了一个一般的框架，涉及矩图两个不同的群体行动。
We prove that a metric of constant scalar curvature on a polarised Kahler manifold is the limit of metrics induced from a specific sequence of projective embeddings; satisfying a condition introduced by H. Luo. This gives, as a Corollary, the uniqueness of constant scalar curvature Kahler metrics in a given rational cohomology class. The proof uses results in the literature on the asymptotics of the Bergman kernel. The arguments are presented in a general framework involving moment maps for two different group actions.