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" counterexample 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.

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