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Bibliographic Details
Main Authors:	Dinh, Tien-Cuong, Ghosh, Subhroshekhar, Wu, Hao
Format:	Preprint
Published:	2024
Subjects:	Complex Variables Algebraic Geometry Probability 31A15, 32C30, 32L10, 60B10, 60D05, 60F10
Online Access:	https://arxiv.org/abs/2402.11672
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Table of Contents:

Let $X$ be a compact Riemann surface and $\mathcal L$ be a positive line bundle on it. We study the conditional zero expectation of all the holomorphic sections of $\mathcal L^n$ which do not vanish on $D$ for some fixed open subset $D$ of $X$. We prove that as $n$ tends to infinity, the zeros of these sections are equidistributed outside $D$ with respect to a probability measure $ν$. This gives rise to a surprising forbidden set.