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

We prove that del Pezzo surfaces of degree 2 over a field k$k$ satisfy weak weak approximation if k$k$ is a number field and the Hilbert property if k$k$ is Hilbertian of characteristic zero, provided that they contain a k$k$‐rational point lying neither on any 4 of the 56 exceptional curves nor on...

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Bibliographic Details
Published in:Proceedings of the London Mathematical Society 2024-05, Vol.128 (5), p.n/a
Main Authors: Demeio, Julian, Streeter, Sam, Winter, Rosa
Format: Article
Language:English
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Summary:We prove that del Pezzo surfaces of degree 2 over a field k$k$ satisfy weak weak approximation if k$k$ is a number field and the Hilbert property if k$k$ is Hilbertian of characteristic zero, provided that they contain a k$k$‐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.
ISSN:0024-6115
1460-244X
DOI:10.1112/plms.12601