2023/03/16 by Demeio, Julian Lawrence, Streeter, Sam, Winter, Rosa · 3 citations
#11G35 (Secondary) #14G05 #14G12 (Primary) #14G25 #14G27 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2303.09299
We prove that del Pezzo surfaces of degree 2 over a field k satisfy weak weak approximation if k is a number field and the Hilbert property if k is Hilbertian of characteristic zero, provided that they contain a 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.