  The moduli space of cubic surfaces in complex projective space is known to be
isomorphic to the quotient of the complex 4-ball by a certain arithmetic group.
We apply Borcherds' techniques to construct automorphic forms for this group
and show that these provide an embedding of the moduli space in 9-dimensional
projective space. We also show that our automorphic forms directly encode the
geometry of cubic surfaces, by showing that each of Cayley's invariants
(certain cross-ratios) is simply a quotient of two of our automorphic forms.
