The moduli of smooth hypersurfaces with level structure

A Javanpeykar, Daniel Loughran

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    Abstract

    We construct the moduli space of smooth hypersurfaces with level N
    structure over Z[1=N]. As an application we show that, for N large enough, the stack of smooth hypersurfaces over Z[1=N] is uniformisable by a smooth ane 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 elds of odd characteristic.
    Original languageEnglish
    Number of pages16
    JournalManuscripta Mathematica
    Early online date19 Dec 2016
    DOIs
    Publication statusPublished - 2016

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