Biholomorphisms between Hartogs domains over homogeneous Siegel domains

TL;DR

This paper characterizes Hartogs domains over homogeneous Siegel domains of type II, describes their automorphism groups, and proves that proper holomorphic maps between such domains are biholomorphisms.

Contribution

It provides a detailed description of automorphism groups and establishes biholomorphic equivalence for proper maps between these domains, advancing understanding of their complex structure.

Findings

Automorphism groups explicitly described

Proper holomorphic maps are biholomorphisms

Characterization of Hartogs domains over Siegel domains

Abstract

In this paper, we characterize the Hartogs domains over homogeneous Siegel domains of type II and explicitly describe their automorphism groups. Moreover we prove that any proper holomorphic map between Hartogs domains over homogeneous Siegel domains over type II is a biholomorphism.