On varieties of Hilbert type
Lior Bary-Soroker, Arno Fehm, Sebastian Petersen (2014)
Annales de l’institut Fourier
Similarity:
A variety over a field is of Hilbert type if is not thin. We prove that if is a dominant morphism of -varieties and both and all fibers , , are of Hilbert type, then so is . We apply this to answer a question of Serre on products of varieties and to generalize a result of Colliot-Thélène and Sansuc on algebraic groups.