Weak Approximation for General Degree Two del Pezzo Surfaces

TL;DR

This paper investigates weak approximation properties of degree two del Pezzo surfaces over function fields, focusing on their rational connectivity and singularities to establish new results for surfaces with square-free discriminant.

Contribution

It introduces a method to prove weak approximation for degree two del Pezzo surfaces with specific singularities and discriminant conditions, advancing understanding of their rational points.

Findings

Weak approximation holds for certain degree two del Pezzo surfaces.

Rational connectivity of the smooth locus is crucial for the proof.

Results apply to surfaces with square-free discriminant.

Abstract

We address weak approximation for certain del Pezzo surfaces defined over the function field of a curve. We study the rational connectivity of the smooth locus of degree two del Pezzo surfaces with two A1 singularities in order to prove weak approximation for degree two del Pezzo surfaces with square-free discriminant.