K3 double structures on Enriques surfaces and their smoothings

Gallego, Francisco Javier; Gonzalez, Miguel; Purnaprajna, Bangere P.

K3 double structures on Enriques surfaces and their smoothings

Authors

Gallego, Francisco Javier

Gonzalez, Miguel

Purnaprajna, Bangere P.

Description

Let $Y$ be a smooth Enriques surface. A $K3$ carpet on $Y$ is a locally Cohen-Macaulay 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 étale $K3$ double cover $X \oversetπ \longrightarrow Y$. We prove that $π$ can be deformed to a family $\SX \longrightarrow \mathbf P^N_{T^*}$ 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.
New title (old title:"Smoothing of $K3$ carpets on Enriques surfaces"). Improved Section 1. Simplified step 2 of proof of theorem 3.2