Weak Approximation for Low Degree del Pezzo Surfaces

Abstract

Let $K=K(C)$ be the function field of a smooth curve $C$. Applying the result of [Xu08], we prove that if $S/K$ is a degree one or two del Pezzo surface which can be completed to a generic family in the parametrizing space over $C$, then weak approximation holds at every place $c\in C$.

13 Pages, 8 figures

References in corpus (1)

• Smoothable del Pezzo surfaces with quotient singularities

Cited by in corpus (2)

• Weak approximation and rationally connected varieties over function fields of curves
• Strong Rational Connectedness of Surfaces