Deformation of spherical CR structures and the universal Picard variety

Jih-Hsin Cheng, I-Hsun Tsai

Published 1998-07-08, updated 2000-05-24Version 2

We study deformation of spherical $CR$ circle bundles over Riemann surfaces of genus > 1. There is a one to one correspondence between such deformation space and the so-called universal Picard variety. Our differential-geometric proof of the structure and dimension of the unramified universal Picard variety has its own interest, and our theory has its counterpart in the Teichmuller theory.