Abstract. We construct holomorphic families of proper holomorphic embeddings of C k into C n (0 < k < n− 1), so that for any two different parameters in the family no holomorphic automorphism of C n can map the image of the corresponding two embeddings onto each other. As an application to the study of the group of holomorphic automorphisms of C n we derive the existence of families of holomorphic C * -actions on C n (n ≥ 5) so that different actions in the family are not conjugate. This result is surprising in view of the long standing Holomorphic Linearization Problem, which in particular asked whether there would be more than one conjugacy class of C * actions on C n (with prescribed linear part at a fixed point).
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.