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arXiv · alg-geom/9709016

A Complex Hyperbolic Structure for Moduli of Cubic Surfaces

Daniel Allcock·James A. Carlson·Domingo Toledo
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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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Daniel Allcock, James A. Carlson, Domingo Toledo. 1997-09-12. A Complex Hyperbolic Structure for Moduli of Cubic Surfaces. https://doi.org/10.1016/s0764-4442(97)82711-5

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