A Hilbert Irreducibility Theorem for Enriques surfaces
Algebraic Geometry
2023-01-18 v4 Number Theory
Abstract
We define the over-exceptional lattice of a minimal algebraic surface of Kodaira dimension 0. Bounding the rank of this object, we prove that a conjecture by Campana and Corvaja--Zannier holds for Enriques surfaces, as well as K3 surfaces of Picard rank greater than 6 apart from a finite list of geometric Picard lattices. Concretely, we prove that such surfaces over finitely generated fields of characteristic 0 satisfy the weak Hilbert property after a finite field extension of the base field. The degree of the field extension can be uniformly bounded.
Cite
@article{arxiv.2109.03726,
title = {A Hilbert Irreducibility Theorem for Enriques surfaces},
author = {Damián Gvirtz-Chen and Giacomo Mezzedimi},
journal= {arXiv preprint arXiv:2109.03726},
year = {2023}
}
Comments
25 pages. Minor corrections. Accepted for publication in Trans. Amer. Math. Soc