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Hyperbolic geometry and moduli of real cubic surfaces

Daniel AllcockJames A. CarlsonDomingo Toledo — 2010

Annales scientifiques de l'École Normale Supérieure

Let 0 be the moduli space of smooth real cubic surfaces. We show that each of its components admits a real hyperbolic structure. More precisely, one can remove some lower-dimensional geodesic subspaces from a real hyperbolic space H 4 and form the quotient by an arithmetic group to obtain an orbifold isomorphic to a component of the moduli space. There are five components. For each we describe the corresponding lattices in PO ( 4 , 1 ) . We also derive several new and several old results on the topology of 0 ....

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