On quotients of bounded homogeneous domains by unipotent discrete groups

TL;DR

This paper investigates the properties of quotients of bounded homogeneous domains by unipotent discrete groups, establishing conditions for holomorphic separability and Steinness, and providing criteria for when these properties hold.

Contribution

It introduces new conditions under which such quotients are holomorphically separable and Stein, advancing understanding of their complex geometric structure.

Findings

Quotients are holomorphically separable.

Necessary condition for quotient to be Stein.

Sufficient conditions identified in specific cases.

Abstract

We show that the quotient of any bounded homogeneous domain by a unipotent discrete group of automorphisms is holomorphically separable. Then we give a necessary condition for the quotient to be Stein and prove that in some cases this condition is also sufficient.