Bergman kernel and complex singularity exponent

2009/11/21 by Bo-Yong Chen, Boyong Chen, Han-Jin Lee +1
Mathematics · #Algebraic and Geometric Analysis #Bergman kernel #Exponent #Geometry and complex manifolds #Holomorphic and Operator Theory #Kernel (algebra) #Mathematical analysis #Mathematics #Philosophy #Pure mathematics #Singularity #math.CV #msc:32A25

paper · pdf · doi:10.1007/s11425-009-0033-7

to appear in Science in China, a special issue dedicated to Professor Zhong Tongde's 80th birthday

arxiv created 2009/11/21 · openalex publication_date 2009/12/01 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We give a precise estimate of the Bergman kernel for the model domain defined by Ω_F=\(z,w)∈ ℂⁿ⁺¹:\rm Imw-|F(z)|²>0\, where F=(f₁,...,f_m) is a holomorphic map from ℂⁿ to ℂ^m, in terms of the complex singularity exponent of F.

Citations

• Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I
• L2 estimates and existence theorems for the ∂ operator
• Estimates of invariant metrics on pseudoconvex domains of dimension two
• The Bergman kernel and biholomorphic mappings of pseudoconvex domains
• On the extension ofL 2 holomorphic functions