Campana points of bounded height on vector group compactifications

Marta Pieropan, Arne Smeets, Sho Tanimoto, Anthony Várilly-Alvarado

Published 2019-08-27Version 1

We initiate a systematic quantitative study on Fano orbifolds of subsets of rational points that are integral with respect to a weighted boundary divisor. We call the points in these sets Campana points. Earlier work of Campana and subsequently Abramovich shows that there are several reasonable competing definitions for Campana points. We use a version that delineates well different types of behaviour of points as the weights on the boundary divisor vary. This prompts a Manin-type conjecture on Fano orbifolds for sets of Campana points that satisfy a klt (Kawamata log terminal) condition. By importing work of Chambert-Loir and Tschinkel to our set-up, we prove a log version of Manin's conjecture for klt Campana points on equivariant compactifications of vector groups.