Observing that the notion of disk in CP^1 is invariant under projective transformations, Kojima, Mizushima and Tan proposed the study of circle packings on surfaces equipped with complex projective structure. The main observation is that combinatorially a circle packing is described by a triangulation of the surface, called the nerve of the circle packing. In the talk we will prove that for a fixed surface S of genus g bigger than one, and for a fixed triangulation T on S, the moduli space of pairs (P,C), where P is a complex projective structure S and C is a circle packing with nerve equal to T, is naturally a manifold of dimension 6g-6. We moreover prove that the circle packing is locally rigid, in the sense that there is no local deformation of C within the projective surface P.
Results presented in the talk are part of a collaboration with Michael Wolf.