Hessians and the moduli space of cubic surfaces

Elisa Dardanelli; Bert van Geemen

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Hessians and the moduli space of cubic surfaces

Elisa Dardanelli·Bert van Geemen

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Abstract

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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BibTeX RIS

Elisa Dardanelli, Bert van Geemen. 2004-09-18. Hessians and the moduli space of cubic surfaces. https://arxiv.org/abs/math/0409322

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