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The probabilistic vs the quantization approach to Kähler–Einstein geometry
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Journal Article
The probabilistic vs the quantization approach to Kähler–Einstein geometry
2024
Overview
In the probabilistic construction of Kähler–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 Kähler–Einstein metrics if it is uniformly Gibbs stable. The proof makes contact with the quantization approach to Kähler–Einstein geometry.
Publisher
Springer Berlin Heidelberg,Springer Nature B.V
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