Year: 2025
Type: preprint
Abstract: We initiate a general quantitative study of sets of $\mathcal{M}$-points, which are special subsets of rational points, generalizing Campana points, Darmon points, and squarefree solutions of Diophantine equations. We propose an asymptotic formula for the number of $\mathcal{M}$-points of bounded height on rationally connected varieties, extending Manin's conjecture as well as its generalization to Campana points by Pieropan, Smeets, Tanimoto and Várilly-Alvarado. Finally, we show that the conjecture explains several previously established results in arithmetic statistics.
Source: arXiv (Cornell University)
Author: Moerman, Boaz
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7110818567
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