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November, 2001 Scalar Curvature and Projective Embeddings, I
S.K. Donaldson
J. Differential Geom. 59(3): 479-522 (November, 2001). DOI: 10.4310/jdg/1090349449


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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S.K. Donaldson. "Scalar Curvature and Projective Embeddings, I." J. Differential Geom. 59 (3) 479 - 522, November, 2001.


Published: November, 2001
First available in Project Euclid: 20 July 2004

zbMATH: 1052.32017
MathSciNet: MR1916953
Digital Object Identifier: 10.4310/jdg/1090349449

Rights: Copyright © 2001 Lehigh University


Vol.59 • No. 3 • November, 2001
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