A Hilbert Irreducibility Theorem for Enriques surfaces

Publikation: Arbeitspapier/Preprint › Preprint

Autoren

  • Damián Gvirtz-Chen
  • Giacomo Mezzedimi

Organisationseinheiten

Externe Organisationen

  • University College London (UCL)
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Details

OriginalspracheEnglisch
Seitenumfang29
PublikationsstatusElektronisch veröffentlicht (E-Pub) - 8 Sept. 2021

Abstract

We investigate geometric versions of Hilbert's Irreducibility Theorem using lattice-theoretic arguments and prove that a conjecture by Campana and Corvaja-Zannier holds for Enriques surfaces, Kummer surfaces, as well as K3 surfaces of Picard number ≥6 apart from a finite list of geometric Néron-Severi 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.

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A Hilbert Irreducibility Theorem for Enriques surfaces. / Gvirtz-Chen, Damián; Mezzedimi, Giacomo.
2021.

Publikation: Arbeitspapier/Preprint › Preprint

Gvirtz-Chen, D., & Mezzedimi, G. (2021). A Hilbert Irreducibility Theorem for Enriques surfaces. Vorabveröffentlichung online. https://doi.org/10.48550/arXiv.2109.03726
Gvirtz-Chen D, Mezzedimi G. A Hilbert Irreducibility Theorem for Enriques surfaces. 2021 Sep 8. Epub 2021 Sep 8. doi: 10.48550/arXiv.2109.03726
Gvirtz-Chen, Damián ; Mezzedimi, Giacomo. / A Hilbert Irreducibility Theorem for Enriques surfaces. 2021.
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