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

2024/07/21 by Liu, Bingxiao, Zielinski, Dominik
#30C15 #30F99 #32A25 #32L05 #60D05 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.15106

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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