On the leading constant in the Manin-type conjecture for Campana points
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.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2021
- DOI:
- 10.48550/arXiv.2104.14946
- arXiv:
- arXiv:2104.14946
- Bibcode:
- 2021arXiv210414946S
- Keywords:
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- Mathematics - Number Theory;
- 11D45 (Primary);
- 14G05 (Secondary)
- E-Print:
- Acta Arithmetica, to appear