Manin's conjecture for a singular quartic del Pezzo surface

TL;DR

This paper proves Manin's conjecture for a specific singular quartic del Pezzo surface by using a conic bundle structure and addressing a divisor problem for binary linear forms.

Contribution

It introduces a novel approach combining conic bundle structures with a new divisor problem result to verify Manin's conjecture for this surface.

Findings

Manin's conjecture holds for the specified surface.

Developed a new divisor problem result for binary linear forms.

Established a method applicable to similar algebraic surfaces.

Abstract

We prove Manin's conjecture for a split singular quartic del Pezzo surface with singularity type $2\Aone$ and eight lines. This is achieved by equipping the surface with a conic bundle structure. To handle the sum over the family of conics, we prove a result of independent interest on a certain restricted divisor problem for four binary linear forms.