Higher Rank Bergman Kernels on Compact Riemann Surfaces

2025/05/18 by Kim, Shin
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.12241

Abstract

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.

Citations

• On the asymptotic expansion of Bergman kernel
• Bergman kernels and local holomorphic Morse inequalities

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