Hole event for random holomorphic sections on compact Riemann surfaces
| Autor: | Dinh, Tien-Cuong, Ghosh, Subhroshekhar, Wu, Hao |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $\nu$. This gives rise to a surprising forbidden set. Comment: fisrt draft |
| Databáze: | arXiv |
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