Weighted Bergman kernels and ⋆-products

2025/03/12 by Andreas Sykora, Sykora, Andreas
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Holomorphic and Operator Theory #Mathematical Physics (math-ph) #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2503.09322

openalex publication_date 2025/03/12 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

Abstract

We calculate the weighted Bergman kernel on a complex domain with a weight of the form ρ=e^-αϕμg, where α is a positive real number, ϕ is a Kähler potential, g is the determinant of the corresponding Kähler metric and μ is a real-valued positive function. Several ⋆-products related to the Bergman kernel are determined. Explicit formulas are provided up to first order.

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