Campana points of bounded height on vector group compactifications

Abstract

We initiate a systematic quantitative study of subsets of rational points that are integral with respect to a weighted boundary divisor on Fano orbifolds. 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.

arXiv comment52 pages; minor revision, changes in the definition of Campana points

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Cited by in corpus (5)

• Paucity of rational points on fibrations with multiple fibres
• Points of bounded height on certain subvarieties of toric varieties
• Semi-integral Brauer-Manin obstruction and quadric orbifold pairs
• Local-global principles for semi-integral points on Markoff orbifold pairs
• Motivic distribution of rational curves and twisted products of toric varieties