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The moduli of smooth hypersurfaces with level structure

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Abstract

We construct the moduli space of smooth hypersurfaces with level N structure over \(\mathbb {Z}[1/N]\). As an application we show that, for N large enough, the stack of smooth hypersurfaces over \(\mathbb {Z}[1/N]\) is uniformisable by a smooth affine scheme. To prove our results, we use the Lefschetz trace formula to show that automorphisms of smooth hypersurfaces act faithfully on their cohomology. We also prove a global Torelli theorem for smooth cubic threefolds over fields of odd characteristic.

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Authors and Affiliations

  1. Institut für Mathematik, Johannes Gutenberg-Universität Mainz, Staudingerweg 9, 55099, Mainz, Germany

    A. Javanpeykar

  2. School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK

    D. Loughran

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  1. A. Javanpeykar
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  2. D. Loughran
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Correspondence to A. Javanpeykar.

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Javanpeykar, A., Loughran, D. The moduli of smooth hypersurfaces with level structure. manuscripta math. 154, 13–22 (2017). https://doi.org/10.1007/s00229-016-0906-3

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  • DOI: https://doi.org/10.1007/s00229-016-0906-3

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