Journal of Differential Geometry

Scalar Curvature and Projective Embeddings, I

S.K. Donaldson


We prove that a metric of constant scalar curvature on a polarised Kähler 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 Kähler 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.

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J. Differential Geom., Volume 59, Number 3 (2001), 479-522.

First available in Project Euclid: 20 July 2004

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Donaldson, S.K. Scalar Curvature and Projective Embeddings, I. J. Differential Geom. 59 (2001), no. 3, 479--522. doi:10.4310/jdg/1090349449.

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