Deformation in the large of some complex manifolds, II

Abstract

The compact complex manifolds considered in this article are principal torus bundles over a torus. We consider the Kodaira Spencer map of the complete Appell Humbert family (introduced by the first author in Part I) and are able to show that we obtain in this way a connected component of the space of complex structures each time that the base dimension is two, the fibre dimension is one, and a suitable topological condition is verified.

23 pages, to appear in the AMS Series 'Contemporary Mathematics',in the Proceedings of the 10th anniversary (2004) Conference for the Mathematics Institute at East China Normal University