On the leading constant in the Manin-type conjecture for Campana points
Volume 204 / 2022
Acta Arithmetica 204 (2022), 317-346
MSC: Primary 11D45; Secondary 14G05.
DOI: 10.4064/aa210430-1-7
Published online: 22 August 2022
Abstract
We compare the Manin-type conjecture for Campana points recently formulated by Pieropan, Smeets, Tanimoto and Várilly-Alvarado with an alternative prediction of Browning and Van Valckenborgh in the special case of the orbifold $(\mathbb P^1,D)$, where $D = \frac {1}{2}[0]+\frac {1}{2}[1]+\frac {1}{2}[\infty ]$. We find that the two predicted leading constants do not agree, and we discuss whether thin sets could explain this discrepancy. Motivated by this, we provide a counterexample to the Manin-type conjecture for Campana points, by considering orbifolds corresponding to squareful values of binary quadratic forms.
