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Abstract. We apply Borcherds' methods for constructing automorphic forms to embed the moduli space M of marked complex cubic surfaces into CP 9 . Specifically, we construct 270 automorphic forms on the complex 4-ball B 4 , automorphic with respect to a particular discrete group Γ. We use the identification from [ACT2] of M with the Baily-Borel compactification of B 4 /Γ. Our forms span a 10-dimensional space, and we exhibit the image of M in CP 9 as the intersection of 270 cubic hypersurfaces. Finally, we interpret the pairwise ratios of our forms as the original invariants of cubic surfaces, the cross-ratios introduced by Cayley. It turns out that this model of M was found by Coble [C] in an entirely different way; see [vG].

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