Calabi-Yau threefolds with a curve of singularities and counterexamples to the Torelli problem

Details Calabi-Yau threefolds with a curve of singularities and counterexamples to the Torelli problem Calabi-Yau threefolds with a curve of singularities and counterexamples to the Torelli problem

1999-01-19

arxiv.org/abs/math/9901078v2

Mathematics

Algebraic Geometry

Improved, shortened version, approx. 10 pages, LaTeX. To appear in Int. J. Math

Scientific paper

10.1017/S0305004100004588

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 complete intersections provide examples of families containing birational varieties. The constructed examples are shown to be non-isomorphic using a specialization argument.

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