On the leading constant in the Manintype conjecture for Campana points
Abstract
We compare the Manintype conjecture for Campana points recently formulated by Pieropan, Smeets, Tanimoto and VárillyAlvarado 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 Manintype conjecture for Campana points, by considering orbifolds corresponding to squareful values of binary quadratic forms.
 Publication:

arXiv eprints
 Pub Date:
 April 2021
 DOI:
 10.48550/arXiv.2104.14946
 arXiv:
 arXiv:2104.14946
 Bibcode:
 2021arXiv210414946S
 Keywords:

 Mathematics  Number Theory;
 11D45 (Primary);
 14G05 (Secondary)
 EPrint:
 Acta Arithmetica, to appear