K3 double structures on Enriques surfaces and their smoothings

Abstract

Let Y be a smooth Enriques surface. A K3 carpet on Y is a double structure on Y with the same invariants as a smooth K3 surface (i.e., regular and with trivial canonical sheaf). The surface Y possesses an etale K3 double cover X ->(pi) over barY. We prove that pi can be deformed to a family X -> P-T*(N) of projective embeddings of K3 surfaces and that any projective K3 carpet on Y arises from such a family as the flat limit of smooth, embedded K3 surfaces.