Rank jumps on elliptic surfaces and the Hilbert property

Daniel Loughran, Cecília Salgado

Research output: Contribution to journalArticlepeer-review


Given an elliptic surface over a number field, we study the collection of fibres whose Mordell-Weil rank is greater than the generic rank. Under suitable assumptions, we show that this collection is not thin. Our results apply to quadratic twist families and del Pezzo surfaces of degree 1.

Original languageEnglish
Pages (from-to)617-638
Number of pages22
JournalAnnales de l'institut Fourier
Issue number2
Early online date7 Jul 2022
Publication statusE-pub ahead of print - 7 Jul 2022


  • elliptic surfaces
  • rank jumps
  • thin sets

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology


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