  Allcock-Carlson-Toledo defined a period map for cubic threefolds which takes
values in a ball quotient of dimension 10. A theorem of Voisin implies that
this is an open embedding. We determine its image and show that on the
algebraic level this amounts to an identification of the algebra of
SL(5,C)-invariant polynomials on the third symmetric power of the dual of the
tautological representation of SL(5,C) with an explicitly described algebra of
meromorphic automorphic forms on the complex 10-ball.
