Quasi-proper meromorphic equivalence relations

TL;DR

This paper extends previous work to establish a broad existence theorem for meromorphic quotients of strongly quasi-proper meromorphic equivalence relations, with applications including a Stein factorization theorem for such maps.

Contribution

It provides new existence results for meromorphic quotients under strongly quasi-proper conditions, generalizing earlier findings and applying to Stein factorization.

Findings

Established a general existence theorem for meromorphic quotients

Proved that generic equivalence classes are pure dimensional with finitely many components

Demonstrated a Stein factorization theorem for strongly quasi-proper maps

Abstract

The aim of this article is to complete results of [M.00] and [B.08] and to show that they imply a rather general existence theorem for meromorphic quotient of strongly quasi-proper meromorphic equivalence relations. In this context, generic equivalence classes are asked to be pure dimensionnal closed analytic subset with finitely many irreducible components. As an application of these methods we prove a Stein factorization theorem for a strongly quasi-proper map