Effectivity for bounds on points of good reduction in the moduli space of hypersurfaces

2024/01/10 by Ji, Caleb
#14G05 (Primary) 11G35 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2401.04981

Abstract

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 ℙⁿ, 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.

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