Weak approximation for del Pezzo surfaces of low degree

TL;DR

This paper proves that weak weak approximation holds for certain low-degree del Pezzo surfaces with conic fibrations, using an arithmetic surjectivity approach inspired by Denef's work.

Contribution

It introduces an arithmetic surjectivity method to establish weak weak approximation for low-degree del Pezzo surfaces with conic fibrations.

Findings

Weak weak approximation holds for general del Pezzo surfaces of degrees 1 and 2 with conic fibrations.

The approach is inspired by Denef's work on arithmetic surjectivity.

The results apply under a general assumption on the fibrations.

Abstract

We prove, via an "arithmetic surjectivity" approach inspired by work of Denef, that weak weak approximation holds for surfaces with two conic fibrations satisfying a general assumption. In particular, weak weak approximation holds for general del Pezzo surfaces of degrees $1$ or $2$ with a conic fibration.