Abstract
The moduli space of stable real cubic surfaces is the quotient of real hyperbolic four-space by a discrete, nonarithmetic group. The volume of the moduli space is 37 π 2/1080 in the metric of constant curvature −1. Each of the five connected components of the moduli space can be described as the quotient of real hyperbolic four-space by a specific arithmetic group. We compute the volumes of these components. To cite this article: D. Allcock et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).
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