Manin’s conjecture predicts the asymptotic behavior of the number of rational points of bounded height on Fano varieties over number fields. We prove this conjecture for a family of nonsplit singular quartic del Pezzo surfaces over arbitrary number fields. For the proof, we parameterize the rational points on such a del Pezzo surface by integral points on a nonuniversal torsor (which is determined explicitly using a Cox ring of a certain type), and we count them using a result of Barroero-Widmer on lattice points in o-minimal structures. This is joint work in progress with Marta Pieropan.
- Number Theory Seminar