Manin's Conjecture for a Singular Sextic del Pezzo Surface

TL;DR

This paper proves Manin's conjecture for a specific singular sextic del Pezzo surface, providing explicit formulas and a meromorphic continuation of the height zeta function.

Contribution

It establishes Manin's conjecture for a singular degree six del Pezzo surface with an A2 singularity, including explicit height zeta function expressions.

Findings

Manin's conjecture verified for the surface

Explicit height zeta function derived

Meromorphic continuation achieved

Abstract

We prove Manin's conjecture for a del Pezzo surface of degree six which has one singularity of type $\mathbf{A}_2$. Moreover, we achieve a meromorphic continuation and explicit expression of the associated height zeta function.