Higher Rank Bergman Kernels on Compact Riemann Surfaces

Shin Kim

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arXiv · 2505.12241

Higher Rank Bergman Kernels on Compact Riemann Surfaces

Shin Kim

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Abstract

Let X be a compact Riemann surface equipped with a real-analytic K\"ahler form $\omega$ 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 $\omega$.

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Shin Kim. 2025-05-18. Higher Rank Bergman Kernels on Compact Riemann Surfaces. https://arxiv.org/abs/2505.12241

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