English

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

R2 v1 2026-07-22T17:09:56.274Z