The probabilistic vs the quantization approach to K\"ahler-Einstein geometry

Robert J. Berman

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arXiv · 2109.06575

The probabilistic vs the quantization approach to K\"ahler-Einstein geometry

Robert J. Berman

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Abstract

In the probabilistic construction of K\"ahler-Einstein metrics on a complex projective algebraic manifold X - involving random point processes on X - a key role is played by the partition function. In this work a new quantitative bound on the partition function is obtained. It yields, in particular, a new direct analytic proof that X admits a K\"ahler-Einstein metrics if it is uniformly Gibbs stable. The proof makes contact with the quantization approach to K\"ahler-Einstein geometry.

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Robert J. Berman. 2021-09-14. The probabilistic vs the quantization approach to K\"ahler-Einstein geometry. https://arxiv.org/abs/2109.06575

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