K3 double structures on Enriques surfaces and their smoothings

2006/04/28 by Gallego, Francisco Javier, Gonzalez, Miguel, Purnaprajna, Bangere P.
#13D10 #14B10 #14J10 #14J28 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0604629

Abstract

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.

Related

• K3 carpets on minimal rational surfaces and their smoothings
• Enriques surfaces with normal K3-like coverings
• Smooth double covers of K3 surfaces
• Which Singular K3 Surfaces Cover an Enriques Surface
• On the Shafarevich conjecture for Enriques surfaces