Manin’s conjecture for a quartic del Pezzo surface with A3 singularity and four lines

Abstract

We establish Manin’s conjecture for a quartic del Pezzo surface split over \({\mathbb{Q}}\) and having a singularity of type A 3 and containing exactly four lines. It is the first example of split singular quartic del Pezzo surface whose universal torsor is not a hypersurface for which Manin’s conjecture is proved.