2023/03/28 by Khelifa, Nazim, Urbanik, David
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2303.16179
Motivated by a question of Baldi-Klingler-Ullmo, we provide a general sufficient criterion for the existence and analytic density of typical Hodge loci associated to a polarizable ℤ-variation of Hodge structures \mathbbV. Our criterion reproves the existing results in the literature on density of Noether-Lefschetz loci. It also applies to understand Hodge loci of subvarieties of Ag . For instance, we prove that for g ≥ 4, if a subvariety S of Ag has dimension at least g then it has an analytically dense typical Hodge locus. This applies for example to the Torelli locus of Ag