Hole event for random holomorphic sections on compact Riemann surfaces
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914684805840896 |
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| author | Dinh, Tien-Cuong Ghosh, Subhroshekhar Wu, Hao |
| author_facet | Dinh, Tien-Cuong Ghosh, Subhroshekhar Wu, Hao |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11672 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hole event for random holomorphic sections on compact Riemann surfaces Dinh, Tien-Cuong Ghosh, Subhroshekhar Wu, Hao Complex Variables Algebraic Geometry Probability 31A15, 32C30, 32L10, 60B10, 60D05, 60F10 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. |
| title | Hole event for random holomorphic sections on compact Riemann surfaces |
| topic | Complex Variables Algebraic Geometry Probability 31A15, 32C30, 32L10, 60B10, 60D05, 60F10 |
| url | https://arxiv.org/abs/2402.11672 |