Actions of groups of birationally extendible automorphisms

Abstract

The origin of this work is found in the study of automorphisms of domains D in Cn, n > 1. For example, suppose for the moment that D is relatively compact and recall that in this case the group Aut(D) of all holomorphic automorphisms is a Lie group acting properly on D in the compact-open topology ([6], see also [19]). It is important to underline the fact that this group is totally real so that, compared to holomorphic actions of complex Lie groups, there is a lack of naturality.