On the Bergman kernel of polarized abelian varieties
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912726592258048 |
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| author | Sun, Jingzhou |
| author_facet | Sun, Jingzhou |
| contents | We prove an explicit formula for the Bergman kernel of polarized abelian varieties. As applications, we show that if two positive line bundles represent the same first Chern class and have identical Bergman kernel functions for some tensor power, then the corresponding powers of the bundles are isomorphic. We also obtain localization results for the maxima and minima of the Bergman kernel function and establish exponential off-diagonal decay estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19003 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Bergman kernel of polarized abelian varieties Sun, Jingzhou Differential Geometry Algebraic Geometry Complex Variables 32A25, 30F45 We prove an explicit formula for the Bergman kernel of polarized abelian varieties. As applications, we show that if two positive line bundles represent the same first Chern class and have identical Bergman kernel functions for some tensor power, then the corresponding powers of the bundles are isomorphic. We also obtain localization results for the maxima and minima of the Bergman kernel function and establish exponential off-diagonal decay estimates. |
| title | On the Bergman kernel of polarized abelian varieties |
| topic | Differential Geometry Algebraic Geometry Complex Variables 32A25, 30F45 |
| url | https://arxiv.org/abs/2511.19003 |