Weak approximation and the Hilbert property for Campana points

TL;DR

This paper explores the relationship between weak approximation and the Hilbert property for Campana points, demonstrating that weak weak approximation implies the Hilbert property and providing examples of Campana orbifolds with non-thin sets of points.

Contribution

It establishes a link between weak weak approximation and the Hilbert property for Campana points and constructs examples of orbifolds with non-thin sets of points.

Findings

Weak weak approximation implies the Hilbert property for Campana points.

Existence of Campana orbifolds with non-thin sets of Campana points.

Abstract

We study weak approximation and the Hilbert property for Campana points, both of importance in recent work on a Manin-type conjecture by Pieropan, Smeets, Tanimoto and Varilly-Alvarado. We show that weak weak approximation implies the Hilbert property for Campana points, and we exploit this to exhibit Campana orbifolds whose sets of Campana points are not thin.