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

Abstract

AbstractWe prove that del Pezzo surfaces of degree 2 over a field satisfy weak weak approximation if is a number field and the Hilbert property if is Hilbertian of characteristic zero, provided that they contain a ‐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.