CALABI YAU THREEFOLDS WITH A CURVE OF SINGULARITIES AND COUNTEREXAMPLES TO THE TORELLI PROBLEM

Birational Calabi{Yau threefolds in the same deformation family provide a \weak " counter-example to the global Torelli problem, as long as they are not isomorphic. In this paper, it is shown that deformations of certain desingularized weighted projective hypersurfaces provide examples of families containing birational varieties. The constructed examples are shown to be nonisomorphic using a specialization argument. The theory of Calabi{Yau threefolds has received a lot of attention in recent years, due to its relation to various elds ranging from birational geometry to superstring theory. One of the important problems in the theory is the