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arXiv · 2407.15106

Semipositive line bundles on punctured Riemann surfaces: Bergman kernels and random zeros

Bingxiao Liu·Dominik Zielinski
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Abstract

We give an extensive study on the Bergman kernel expansions and the random zeros associated with the high tensor powers of a semipositive line bundle on a complete punctured Riemann surface. We prove several results for the zeros of Gaussian holomorphic sections in the semi-classical limit, including the equidistribution, large deviation estimates, central limit theorem, and number variances.

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Bingxiao Liu, Dominik Zielinski. 2024-07-21. Semipositive line bundles on punctured Riemann surfaces: Bergman kernels and random zeros. https://arxiv.org/abs/2407.15106

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