@article{527b64ae90134659aa3e621da254148d,

title = "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 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.",

keywords = "11G35, 11G50 (primary), 14G05, 14G10 (secondary)",

author = "M. Pieropan and Arne Smeets and Sho Tanimoto and Anthony V{\'a}rilly-Alvarado",

note = "Funding Information: The authors would like to thank Tim Browning, Fr?d?ric Campana, Ulrich Derenthal, Yoshishige Haraoka, and Brian Lehmann for useful discussions and for their feedback. We thank Dan Loughran for his valuable comments and for pointing out a mistake in an early version of this paper. We also thank the referee for very careful and thoughtful comments which significantly improved the exposition of the paper and generalized our main?theorems. We thank for their hospitality the organizers of the trimester program ?Reinventing Rational Points? at the Institut Henri Poincar?, Daniel Huybrechts at the Universit?t Bonn, and Michael Stoll, organizer of the workshop ?Rational Points 2019? at Schney, where parts of this paper were?completed. Publisher Copyright: {\textcopyright} 2020 The Authors. Proceedings of the London Mathematical Society is copyright {\textcopyright} London Mathematical Society.",

year = "2021",

month = jul,

doi = "10.1112/plms.12391",

language = "English",

volume = "123",

pages = "57--101",

journal = "Proceedings of the London Mathematical Society",

issn = "0024-6115",

publisher = "Oxford University Press",

number = "1",

}