A Complex Hyperbolic Structure for Moduli of Cubic Surfaces
Daniel Allcock, James A. Carlson, Domingo Toledo
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.
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