# On the equidistribution of some Hodge loci

@article{Tayou2018OnTE, title={On the equidistribution of some Hodge loci}, author={Salim Tayou}, journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)}, year={2018}, volume={2020}, pages={167 - 194} }

Abstract We prove the equidistribution of the Hodge locus for certain non-isotrivial, polarized variations of Hodge structure of weight 2 with h 2 , 0 = 1 {h^{2,0}=1} 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 K3 surfaces.

## 8 Citations

### On the distribution of the Hodge locus

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. Given a polarizable Z -variation of Hodge structures V over a complex smooth quasi-projective base S , a classical result of Cattani, Deligne and Kaplan says that its Hodge locus (i.e. the locus…

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### Exceptional jumps of Picard ranks of reductions of K3 surfaces over number fields

- MathematicsForum of Mathematics, Pi
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Abstract Given a K3 surface X over a number field K with potentially good reduction everywhere, we prove that the set of primes of K where the geometric Picard rank jumps is infinite. As a corollary,…

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The Hodge theory of complex algebraic varieties is at heart a transcendental comparison of two algebraic structures. We survey the recent advances bounding this transcendence, mainly due to the…

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Let X→C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}…

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