Weak approximation and the Hilbert property for 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.

arXiv comment23 pages, minor revisions; to appear in Michigan Mathematical Journal

References in corpus (5)

• Nested efficient congruencing and relatives of Vinogradov's mean value theorem
• Birational geometry for number theorists
• The Hilbert Property for integral points of affine smooth cubic surfaces
• Campana points and powerful values of norm forms
• Arithmetic of higher-dimensional orbifolds and a mixed Waring problem

Cited by in corpus (3)

• Campana points and powerful values of norm forms
• Sums of four squareful numbers
• Campana points, Height zeta functions, and log Manin's conjecture