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In this paper we show that the moduli space of nodal cubic surfaces is  isomorphic to a quotient of a 4-dimensional complex ball by an arithmetic  subgroup of the unitary group. This complex ball uniformization uses the periods  of certain  K  3 surfaces which are naturally associated to cubic  surfaces. A similar uniformization is given for different covers of the moduli  space corresponding to geometric markings of the Picard group or a choice of a  line on the surface. We also give a detailed description of the boundary  components corresponding to singular surfaces.

A complex ball uniformization of the moduli space of cubic surfaces via periods of K 3 surfaces