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arXiv · 0804.0668

Small Resolutions and Non-Liftable Calabi-Yau threefolds

S. Cynk·D. van Straten
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Abstract

We use properties of small resolutions of the ordinary double point in dimension three to construct smooth non-liftable Calabi-Yau threefolds. In particular, we construct a smooth projective Calabi-Yau threefold over $\F_3$ that does not lift to characteristic zero and a smooth projective Calabi-Yau threefold over $\F_5$ having an obstructed deformation. We also construct many examples of smooth Calabi-Yau algebraic spaces over $\F_p$ that do not lift to algebraic spaces in characteristic zero.

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S. Cynk, D. van Straten. 2008-04-09. Small Resolutions and Non-Liftable Calabi-Yau threefolds. https://arxiv.org/abs/0804.0668

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