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Small resolutions and non-liftable Calabi-Yau threefolds

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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 \({\mathbb{F}_3}\) that does not lift to characteristic zero and a smooth projective Calabi-Yau threefold over \({\mathbb{F}_5}\) having an obstructed deformation. We also construct many examples of smooth Calabi-Yau algebraic spaces over \({\mathbb{F}_p}\) that do not lift to algebraic spaces in characteristic zero.

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Authors and Affiliations

  1. Instytut Matematyki, Uniwersytetu Jagiellońskiego, ul. Łlojasiewicza 6, 30-348, Kraków, Poland

    Sławomir Cynk

  2. Institute of Mathematics of the Polish Academy of Sciences, ul. Śniadeckich 8, 00-956, Warsaw, Poland

    Sławomir Cynk

  3. Fachbereich 08, AG Algebraische Geometrie, Johannes Gutenberg-Universität, 55099, Mainz, Germany

    Duco van Straten

Authors
  1. Sławomir Cynk
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  2. Duco van Straten
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Correspondence to Sławomir Cynk.

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Cynk, S., van Straten, D. Small resolutions and non-liftable Calabi-Yau threefolds. manuscripta math. 130, 233–249 (2009). https://doi.org/10.1007/s00229-009-0293-0

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  • DOI: https://doi.org/10.1007/s00229-009-0293-0

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