Bergman kernels of Monomial Polyhedra
Debraj Chakrabarti, Isaac Cinzori, Ishani Gaidhane, Jonathan Gregory,, Mary Wright
TL;DR
This paper explicitly computes the Bergman kernels for monomial polyhedra, a class of pseudoconvex Reinhardt domains, revealing their rational function structure through Bell's transformation formula.
Contribution
It provides the first explicit formulas for Bergman kernels of monomial polyhedra using Bell's transformation, advancing understanding of these domains.
Findings
Bergman kernels are rational functions
Explicit formulas derived using Bell's transformation
Enhances understanding of pseudoconvex Reinhardt domains
Abstract
The Bergman kernels of monomial polyhedra are explicitly computed. Monomial polyhedra are a class of bounded pseudoconvex Reinhardt domains defined as sublevel sets of Laurent monomials. Their kernels are rational functions and are obtained by an application of Bell's transformation formula.
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Taxonomy
TopicsHolomorphic and Operator Theory · Geometry and complex manifolds · Algebraic and Geometric Analysis