Effectivity for bounds on points of good reduction in the moduli space of hypersurfaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909311491375104 |
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| author | Ji, Caleb |
| author_facet | Ji, Caleb |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04981 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Effectivity for bounds on points of good reduction in the moduli space of hypersurfaces Ji, Caleb Algebraic Geometry Number Theory 14G05 (Primary) 11G35 (Secondary) 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. |
| title | Effectivity for bounds on points of good reduction in the moduli space of hypersurfaces |
| topic | Algebraic Geometry Number Theory 14G05 (Primary) 11G35 (Secondary) |
| url | https://arxiv.org/abs/2401.04981 |