Canonical coordinates and Bergman metrics

Abstract

In this paper we will discuss local coordinates canonically corresponding to a Kahler metric. We will also discuss and prove the $C^{\infty }$ convergence of Bergman metrics following Tian's result on $C^2$ convergence of Bergman metrics. At the end, we present an interesting characterization of ample line bundle that could be useful in arithmetic geometry.

44 pages, LaTex

Cited by in corpus (5)

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• A closed formula for the asymptotic expansion of the Bergman kernel
• Space of Kähler metrics (V)-- Kähler quantization
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• Weighted Bergman kernels on orbifolds