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 H^2(X, Z) for some of these surfaces X.

Smooth double covers of K3 surfaces / A. Garbagnati. - In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE. - ISSN 2036-2145. - 19:1(2019), pp. 345-386. [10.2422/2036-2145.201701_013]

Smooth double covers of K3 surfaces

A. Garbagnati
2019

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 H^2(X, Z) for some of these surfaces X.
K3 surfaces; Double covers; Bidouble covers
Settore MAT/03 - Geometria
11-mag-2016
https://arxiv.org/pdf/1605.03438.pdf
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/557169
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