Campana points of bounded height on vector group compactifications

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 comp...

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Bibliographic Details
Published in:Proceedings of the London Mathematical Society 2021-07, Vol.123 (1), p.57-101
Main Authors: Pieropan, Marta, Smeets, Arne, Tanimoto, Sho, Várilly‐Alvarado, Anthony
Format: Article
Language:English
Subjects:
11G35
11G50 (primary)
14G05
14G10 (secondary)
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Summary: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 behavior 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 setup, we prove a log version of Manin's conjecture for klt Campana points on equivariant compactifications of vector groups.
ISSN:0024-6115
1460-244X
DOI:10.1112/plms.12391