On varieties of Hilbert type

Lior Bary-Soroker, Arno Fehm, Sebastian Petersen

Research output: Contribution to journalArticlepeer-review


A variety X over a field Κ is of Hilbert type if X(Κ) is not thin. We prove that if f : X → S is a dominant morphism of Κ-varieties and both S and all fibers f-1(s), s ∈ S(Κ), 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-Thélène and Sansuc on algebraic groups.

Original languageEnglish
Pages (from-to)1893-1901
Number of pages9
JournalAnnales de l'Institut Fourier
Issue number5
StatePublished - 2014


  • Algebraic group
  • Hilbertian field
  • Thin set
  • Variety of Hilbert type


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