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arXiv · 1511.09291

The moduli of smooth hypersurfaces with level structure

Ariyan Javanpeykar·Daniel Loughran
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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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Ariyan Javanpeykar, Daniel Loughran. 2015-11-30. The moduli of smooth hypersurfaces with level structure. https://arxiv.org/abs/1511.09291

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