On the equidistribution of some Hodge loci
Salim Tayou

TL;DR
This paper proves the equidistribution of Hodge loci in certain variations of Hodge structure over complex curves, providing asymptotic growth results and implications for elliptic fibrations in K3 surface families.
Contribution
It establishes the equidistribution of Hodge loci for specific non-isotrivial polarized variations of Hodge structure of weight 2 with h^{2,0}=1.
Findings
Hodge loci are equidistributed in the specified setting
Asymptotic growth of Hodge loci under norm conditions
Elliptic fibrations are equidistributed in certain K3 surface families
Abstract
We prove the equidistribution of the Hodge locus for certain non-isotrivial, polarized variations of Hodge structure of weight with over complex, quasi-projective curves. Given some norm condition, we also give an asymptotic on the growth of the Hodge locus. In particular, this implies the equidistribution of elliptic fibrations in quasi-polarized, non-isotrivial families of surfaces.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Analytic Number Theory Research · Algebraic Geometry and Number Theory
