Weak weak approximation and the Hilbert property for degree 2 del Pezzo surfaces

Julian Demeio, Sam Streeter, Rosa Winter

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We prove that del Pezzo surfaces of degree 2 over a field (Formula presented.) satisfy weak weak approximation if (Formula presented.) is a number field and the Hilbert property if (Formula presented.) is Hilbertian of characteristic zero, provided that they contain a (Formula presented.) -rational point lying neither on any 4 of the 56 exceptional curves nor on the ramification divisor of the anticanonical morphism. This builds upon results of Manin, Salgado–Testa–Várilly-Alvarado, and Festi–van Luijk on the unirationality of such surfaces, and upon work of the first two authors verifying weak weak approximation under the assumption of a conic fibration.

Original languageEnglish
Article numbere12601
JournalProceedings of the London Mathematical Society
Issue number5
Early online date15 May 2024
Publication statusPublished - 31 May 2024

ASJC Scopus subject areas

  • General Mathematics

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