Semipositive line bundles on punctured Riemann surfaces: Bergman kernels and random zeros
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909263674212352 |
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| author | Liu, Bingxiao Zielinski, Dominik |
| author_facet | Liu, Bingxiao Zielinski, Dominik |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15106 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Semipositive line bundles on punctured Riemann surfaces: Bergman kernels and random zeros Liu, Bingxiao Zielinski, Dominik Complex Variables Differential Geometry 32A25, 30C15, 30F99, 32L05, 60D05 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. |
| title | Semipositive line bundles on punctured Riemann surfaces: Bergman kernels and random zeros |
| topic | Complex Variables Differential Geometry 32A25, 30C15, 30F99, 32L05, 60D05 |
| url | https://arxiv.org/abs/2407.15106 |