Hessians and the moduli space of cubic surfaces
Algebraic Geometry
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0409322,
title = {Hessians and the moduli space of cubic surfaces},
author = {Elisa Dardanelli and Bert van Geemen},
journal= {arXiv preprint arXiv:math/0409322},
year = {2007}
}
Comments
20 pages