Quasi-proper meromorphic equivalence relations

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