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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.04981 |
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Table of Contents:
- Let $S$ be a finite set of primes. For sufficiently large $n$ and $d$, Lawrence and Venkatesh proved that in the moduli space of hypersurfaces of degree $d$ in $\mathbb{P}^n$, the locus of points with good reduction outside $S$ is not Zariski dense. We make this result effective by computing explicit values of $n$ and $d$ for which this statement holds. We accomplish this by giving a more precise computation and analysis of the Hodge numbers of these hypersurfaces and check that they satisfy certain bounds.