Small Resolutions and Non-Liftable Calabi-Yau threefolds

S. Cynk; D. van Straten

Small Resolutions and Non-Liftable Calabi-Yau threefolds

Algebraic Geometry 2008-04-09 v2 Number Theory

Authors: S. Cynk , D. van Straten

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.

Keywords

small resolutions ordinary double point Calabi-Yau threefolds non-liftable characteristic zero obstructed deformation algebraic spaces

Cite

@article{arxiv.0804.0668,
  title  = {Small Resolutions and Non-Liftable Calabi-Yau threefolds},
  author = {S. Cynk and D. van Straten},
  journal= {arXiv preprint arXiv:0804.0668},
  year   = {2008}
}

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16 pages, 3 figures

Small Resolutions and Non-Liftable Calabi-Yau threefolds

Abstract

Keywords

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