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arXiv · 2109.03726

A Hilbert Irreducibility Theorem for Enriques surfaces

Damián Gvirtz-Chen·Giacomo Mezzedimi
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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.

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BibTeXRIS

Damián Gvirtz-Chen, Giacomo Mezzedimi. 2021-09-08. A Hilbert Irreducibility Theorem for Enriques surfaces. https://arxiv.org/abs/2109.03726

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