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.
Hessians and the moduli space of cubic surfaces / E. Dardanelli, B. van Geemen (CONTEMPORARY MATHEMATICS). - In: Algebraic geometry / [a cura di] JongHae Keum, Shigeyuki Kondo. - Providence : American Mathematical Society, 2007. - ISBN 978-0-8218-4201-0. - pp. 17-36 (( convegno Korea-Japan Conference in honor of Igor Dolgachev's 60th birthday tenutosi a Seoul nel 2004.
Hessians and the moduli space of cubic surfaces
B. van GeemenUltimo
2007
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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