Smooth double covers of K3 surfaces

2016/05/11 by Garbagnati, Alice · 1 citation
#14J27 #14J28 (Primary) #14J29 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.03438

Abstract

In this paper we classify the topological invariants of the possible branch loci of a smooth double cover f:X→ Y of a K3 surface Y. We describe some geometric properties of X which depend on the properties of the branch locus. We give explicit examples of surfaces X with Kodaira dimension 1 and 2 obtained as double cover of K3 surfaces and we describe some of them as bidouble cover of rational surfaces. Then, we classify the K3 surfaces which admit smooth double covers X satisfying certain conditions; under these conditions the surface X is of general type, h^1,0(X)=0 and h^2,0(X)=2. We discuss the variation of the Hodge structure of H²(X,ℤ) for some of these surfaces X.

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