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arXiv · 1302.4038

On varieties of Hilbert type

Lior Bary-Soroker·Arno Fehm·Sebastian Petersen
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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.

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Lior Bary-Soroker, Arno Fehm, Sebastian Petersen. 2013-02-17. On varieties of Hilbert type. https://arxiv.org/abs/1302.4038

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