On the equidistribution of some Hodge loci

Salim Tayou

On the equidistribution of some Hodge loci

Algebraic Geometry 2019-09-02 v2 Number Theory

Authors: Salim Tayou

Abstract

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

Keywords

hodge locus equidistribution variations of hodge structure k3 surfaces elliptic fibrations quasi-projective curves

Cite

@article{arxiv.1801.05751,
  title  = {On the equidistribution of some Hodge loci},
  author = {Salim Tayou},
  journal= {arXiv preprint arXiv:1801.05751},
  year   = {2019}
}

Comments

33 pages. To appear in Journal f\"ur die reine und angewandte Mathematik (Crelles Journal)

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