On the leading constant in the Manin-type conjecture for Campana points. (English) Zbl 1517.11072
Summary: We compare the Manin-type conjecture for Campana points recently formulated by M. Pieropan et al. [Proc. Lond. Math. Soc. (3) 123, No. 1, 57–101 (2021; Zbl 1479.11116)] with an alternative prediction of T. D. Browning and K. Van Valckenborgh [Exp. Math. 21, No. 2, 204–211 (2012; Zbl 1327.11022)] 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 squarefull values of binary quadratic forms.
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