[PDF] Weak weak approximation and the Hilbert property for degree-two del Pezzo surfaces-论文阅读讨论-ReadPaper

摘要

We prove that del Pezzo surfaces of degree $2$ over a field $k$ satisfy weakweak approximation if $k$ is a number field and the Hilbert property if $k$ isHilbertian of characteristic zero, provided that they contain a $k$-rationalpoint lying neither on any $4$ of the $56$ exceptional curves nor on theramification divisor of the anticanonical morphism. This builds upon results ofManin, Salgado--Testa--V\'arilly-Alvarado, and Festi--van Luijk on theunirationality of such surfaces, and upon work of the first two authorsverifying weak weak approximation under the assumption of conic bundlestructure.

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