The degree of biholomorphisms of quasi-Reinhardt domains fixing the origin

TL;DR

This paper characterizes biholomorphisms of quasi-Reinhardt domains fixing the origin using polynomial Bergman representative coordinates, establishing a degree bound based on resonance order.

Contribution

It provides a polynomial description of biholomorphisms with a degree bound, linking domain symmetries to resonance order.

Findings

Biholomorphisms are polynomial mappings.

Degree of these mappings is bounded by resonance order.

Bergman representative coordinates are key to this description.

Abstract

We give a description of biholomorphisms of quasi-Reinhardt domains fixing the origin via Bergman representative coordinates, which are shown to be polynomial mappings with a degree bound given by the so-called "resonance order".