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The \(F\)-pure threshold of a Calabi–Yau hypersurface

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Abstract

We compute the \(F\)-pure threshold of the affine cone over a Calabi–Yau hypersurface, and relate it to the order of vanishing of the Hasse invariant on the versal deformation space of the hypersurface.

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Acknowledgments

We thank Mircea Mustaţă for raising the question for elliptic curves at the AMS-MRC workshop on Commutative Algebra, Snowbird, 2010, the workshop participants, and the American Mathematical Society. We also thank Johan de Jong for a useful conversation.

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI, 48109, USA

    Bhargav Bhatt

  2. Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, UT, 84112, USA

    Anurag K. Singh

Authors
  1. Bhargav Bhatt
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  2. Anurag K. Singh
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Corresponding author

Correspondence to Bhargav Bhatt.

Additional information

B. Bhatt was supported by NSF Grants DMS 1160914 and DMS 1128155, and A. K. Singh by NSF Grant DMS 1162585. B. Bhatt and A. K. Singh were supported by NSF Grant 0932078000 while in residence at MSRI.

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Bhatt, B., Singh, A.K. The \(F\)-pure threshold of a Calabi–Yau hypersurface. Math. Ann. 362, 551–567 (2015). https://doi.org/10.1007/s00208-014-1129-0

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  • DOI: https://doi.org/10.1007/s00208-014-1129-0

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