Higher Rank Bergman Kernels on Compact Riemann Surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909628094218240 |
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| author | Kim, Shin |
| author_facet | Kim, Shin |
| contents | Let X be a compact Riemann surface equipped with a real-analytic Kähler form $ω$ and let E be a holomorphic vector bundle over $X$ equipped with a real-analytic Hermitian metric $h$. Suppose that the curvature of $h$ is Griffiths-positive. We prove the existence of a global asymptotic expansion in powers of $k$ of the Bergman kernel associated to $(S^k E, S^k h)$ and $ω$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12241 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher Rank Bergman Kernels on Compact Riemann Surfaces Kim, Shin Complex Variables Algebraic Geometry Let X be a compact Riemann surface equipped with a real-analytic Kähler form $ω$ and let E be a holomorphic vector bundle over $X$ equipped with a real-analytic Hermitian metric $h$. Suppose that the curvature of $h$ is Griffiths-positive. We prove the existence of a global asymptotic expansion in powers of $k$ of the Bergman kernel associated to $(S^k E, S^k h)$ and $ω$. |
| title | Higher Rank Bergman Kernels on Compact Riemann Surfaces |
| topic | Complex Variables Algebraic Geometry |
| url | https://arxiv.org/abs/2505.12241 |