Hessians and the moduli space of cubic surfaces

Details Hessians and the moduli space of cubic surfaces Hessians and the moduli space of cubic surfaces

2004-09-18

arxiv.org/abs/math/0409322v1

Mathematics

Algebraic Geometry

20 pages

Scientific paper

The Hessian of a general cubic surface is a nodal quartic surface, hence its desingularisation is a K3 surface. We determine the transcendental lattice of the Hessian K3 surface for various cubic surfaces (with nodes and/or Eckardt points for example). Classical invariant theory shows that the moduli space of cubic surfaces is a weighted projective space. We describe the singular locus and some other subvarieties of the moduli space.

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