Bergman kernels of elementary Reinhardt domains

Debraj Chakrabarti, Austin Konkel, Meera Mainkar and Evan Miller

Vol. 306 (2020), No. 1, 67–93

DOI: 10.2140/pjm.2020.306.67

Abstract

We study the Bergman kernel of certain domains in ${ℂ}^n$, called elementary Reinhardt domains, generalizing the classical Hartogs triangle. For some elementary Reinhardt domains, we explicitly compute the kernel, which is a rational function of the coordinates. For some other such domains, we show that the kernel is not a rational function. For a general elementary Reinhardt domain, we obtain a representation of the kernel as an infinite series.

Keywords

Bergman kernel

Mathematical Subject Classification 2010

Primary: 32A25

Secondary: 32A07

Milestones

Received: 6 September 2019

Revised: 3 January 2020

Accepted: 12 January 2020

Published: 14 June 2020