Levi problem and semistable quotients

TL;DR

This paper investigates the class of complex spaces formed as semistable quotients of Stein manifolds by reductive group actions, demonstrating that pseudoconvex unramified domains over such spaces also belong to this class.

Contribution

It establishes that all pseudoconvex unramified domains over semistable quotients are themselves semistable quotients, expanding understanding of their structure.

Findings

Pseudoconvex unramified domains over ${ m extbf{X}}$ are in ${ m extbf{Q}}_G$

Semistable quotients are stable under pseudoconvex unramified coverings

The class ${ m extbf{Q}}_G$ is closed under certain domain extensions

Abstract

A complex space $X$ is in class ${\mathcal Q}_G$ if it is a semistable quotient of the complement to an analytic subset of a Stein manifold by a holomorphic action of a reductive complex Lie group $G$. It is shown that every pseudoconvex unramified domain over $X$ is also in ${\mathcal Q}_G$.