1. A Hilbert irreducibility theorem for Enriques surfaces
- Author
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Gvirtz-Chen, Damián and Mezzedimi, Giacomo
- Subjects
Mathematics - Algebraic Geometry ,Mathematics::Algebraic Geometry ,Mathematics - Number Theory ,Applied Mathematics ,General Mathematics ,FOS: Mathematics ,14J28, 14G05 (Primary) 14J27, 11R45 (Secondary) ,Number Theory (math.NT) ,Algebraic Geometry (math.AG) - 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., 25 pages. Minor corrections. Accepted for publication in Trans. Amer. Math. Soc
- Published
- 2023