English

The double cover of cubic surfaces branched along their Hessian

Algebraic Geometry 2010-12-21 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1012.4242,
  title  = {The double cover of cubic surfaces branched along their Hessian},
  author = {Atsushi Ikeda},
  journal= {arXiv preprint arXiv:1012.4242},
  year   = {2010}
}

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39 pages