A Complex Hyperbolic Structure for Moduli of Cubic Surfaces
arXiv:alg-geom/9709016 · doi:10.1016/S0764-4442(97)82711-5
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.
Six pages, plain tex, available at http://www.math.utah.edu/~allcock
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- New complex- and quaternion-hyperbolic reflection groups