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arXiv · 2211.04091

Peak sections and Bergman kernels on K\"ahler manifolds with complex hyperbolic cusps

Shengxuan Zhou
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Abstract

By revisiting Tian's peak section method, we obtain a localization principle of the Bergman kernels on K\"ahler manifolds with complex hyperbolic cusps, which is a generalization of Auvray-Ma-Marinescu's localization result Bergman kernels on punctured Riemann surfaces [Auvray-Ma-Marinescu, Math. Ann., 2021]. Then we give some further estimates when the metric on the complex hyperbolic cusp is a K\"ahler-Einstein metric or when the manifold is a quotient of the complex ball. By applying our method directly to Poincar\'e type cusps, we also get a partial localization result.

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Shengxuan Zhou. 2022-11-08. Peak sections and Bergman kernels on K\"ahler manifolds with complex hyperbolic cusps. https://arxiv.org/abs/2211.04091

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