The double cover of cubic surfaces branched along their Hessian

Details The double cover of cubic surfaces branched along their Hessian The double cover of cubic surfaces branched along their Hessian

2010-12-20

arxiv.org/abs/1012.4242v1

Mathematics

Algebraic Geometry

39 pages

Scientific paper

We prove the relation between the Hodge structure of the double cover of a nonsingular cubic surface branched along its Hessian and the Hodge structure of the triple cover of the ambient projective space branched along the cubic surface. And we introduce a method to study the infinitesimal variations of Hodge structure of the double cover of the cubic surface. Using these results, we compute the N\'{e}ron-Severi lattices for the double cover of a generic cubic surface and the Fermat cubic surface.

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