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arXiv · 2210.16601

Fiberwise Bergman kernels, vector bundles, and log-subharmonicity

Shijie Bao·Qi'an Guan
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Abstract

In this article, we consider Bergman kernels related to modules at boundary points for singular hermitian metrics on holomorphic vector bundles, and obtain a log-subharmonicity property of the Bergman kernels. As applications, we obtain a lower estimate of weighted $L^2$ integrals on sublevel sets of plurisubharmonic functions, and reprove an effectiveness result of the strong openness property of the modules.

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Shijie Bao, Qi'an Guan. 2022-10-29. Fiberwise Bergman kernels, vector bundles, and log-subharmonicity. https://arxiv.org/abs/2210.16601

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