Deformation of spherical CR structures and the universal Picard variety

We study deformations of a spherical CR circle bundle over a Riemann surface of genus > 1. Roughly speaking, there is a diffeomorphism between such a deformation space and the unramified universal Picard variety. On the way to the latter, are actually give a differential-geometric proof of the structure and dimension of the unramified universal Picard variety.