Volume of the space of real cubic surfaces

James Carlson
Clay Mathematics Institute and University of Utah, USA
 

Abstract

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We show that the moduli space of real cubic surfaces has a natural real hyperbolic structure, hence a natural volume.  This volume can be computed exactly.  As a result one can say, for instance, that the part of the moduli space corresponding to cubics with twenty-seven real lines constitutes about two percent of the total volume.