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Non-liftable Calabi-Yau spaces. (English) Zbl 1254.14047

The article under review constructs new examples of non-liftable Calabi-Yau spaces in finite characteristic. The technique is to construct a rigid Calabi-Yau space over some number field that reduces to a nodal model of the given Calabi-Yau space \(X\) in characteristic \(p>0\). Rigid Calabi-Yau spaces are constructed working with fiber products of rational elliptic surfaces.
Theorem: For each prime \(p<100\), (with some exceptions), there is a non-liftable Calabi-Yau three-dimensional Calabi-Yau space in characteristic \(p>0\).
These results are tabulated. As for the proof of non-liftability, the main idea comes from the article [S. Cynk and D. van Straten, Manuscr. Math. 130, No. 2, 233–249 (2009; Zbl 1177.14081)].

MSC:

14J32 Calabi-Yau manifolds (algebro-geometric aspects)

Citations:

Zbl 1177.14081
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References:

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