A Hilbert Irreducibility Theorem for Enriques surfaces

Autor:	Gvirtz-Chen, Damián, Mezzedimi, Giacomo
Rok vydání:	2021
Předmět:	Mathematics - Algebraic Geometry Mathematics - Number Theory 14J28 14G05 (Primary) 14J27 11R45 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 25 pages. Minor corrections. Accepted for publication in Trans. Amer. Math. Soc
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2109.03726 Zobrazit plný text záznamu View this record from Arxiv