Manin's conjecture for a quartic del Pezzo surface with A_3 singularity and four lines

TL;DR

This paper proves Manin's conjecture for a specific quartic del Pezzo surface with an A_3 singularity and four lines, marking the first such split singular surface with a non-hypersurface universal torsor where the conjecture is confirmed.

Contribution

It provides the first proof of Manin's conjecture for a split singular quartic del Pezzo surface with a non-hypersurface universal torsor.

Findings

Manin's conjecture is verified for the specified surface.

The universal torsor of this surface is not a hypersurface.

This work extends the class of surfaces for which Manin's conjecture is proven.

Abstract

We establish Manin's conjecture for a quartic del Pezzo surface split over 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.