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Summary: The Complex Hyperbolic Geometry of the
Moduli Space of Cubic Surfaces
Daniel Allcock, James A. Carlson, and Domingo Toledo
To Herb Clemens on his 60th birthday
Contents
1. Introduction
2. Moduli of smooth cubic surfaces
3. Moduli of stable cubic surfaces
4. Proofs of lemmas
5. Topology of nodal degenerations
6. Fractional di erentials and extension of the period map
7. The monodromy group and hyperplane con guration
8. Cuspidal degenerations
9. Proof of the main theorem
10. The universal cubic surface
11. Automorphisms of cubic surfaces
12. Index of notation
1: Introduction
A classical theorem of great beauty describes the connection between cubic curves and hy-
perbolic geometry: the moduli space of the former is a quotient of the complex hyperbolic line
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