On varieties of Hilbert type
Algebraic Geometry
2013-03-12 v2 Number Theory
Abstract
A variety X over a field K is of Hilbert type if the set of rational points X(K) is not thin. We prove that if f: X\to S is a dominant morphism of K-varieties and both S and all fibers f^{-1}(s), s in S(K), are of Hilbert type, then so is X. We apply this to answer a question of Serre on products of varieties and to generalize a result of Colliot-Th'el`ene and Sansuc on algebraic groups.
Cite
@article{arxiv.1302.4038,
title = {On varieties of Hilbert type},
author = {Lior Bary-Soroker and Arno Fehm and Sebastian Petersen},
journal= {arXiv preprint arXiv:1302.4038},
year = {2013}
}
Comments
We added a corollary on homogeneous spaces, and slightly generalized the formulation of the main result