English

A Complex Hyperbolic Structure for Moduli of Cubic Surfaces

alg-geom 2009-10-30 v1 Algebraic Geometry

Abstract

We show that the moduli space M of marked cubic surfaces is biholomorphic to the quotient by a discrete group generated by complex reflections of the complex four-ball minus the reflection hyperplanes of the group. Thus M carries a complex hyperbolic structure: an (incomplete) metric of constant holomorphic sectional curvature.

Keywords

Cite

@article{arxiv.alg-geom/9709016,
  title  = {A Complex Hyperbolic Structure for Moduli of Cubic Surfaces},
  author = {Daniel Allcock and James A. Carlson and Domingo Toledo},
  journal= {arXiv preprint arXiv:alg-geom/9709016},
  year   = {2009}
}

Comments

Six pages, plain tex, available at http://www.math.utah.edu/~allcock