abstract: We characterize the holomorphic actions of PSL(2,C) on complex compact threefolds that have an open orbit or, equivalently, the equivariant compactifications of the three-dimensional homogenous spaces of PSL(2,C). The main tool in this study is a classification of the germs of Lie algebras of holomorphic vector fields -isomorphic to the Lie algebra of PSL(2,C)- that generate a true, and not multivalued, action.
guillot.pdf