Holmstrom Manin conjecture

arXiv:1009.2364 Manin’s Conjecture for a Singular Sextic del Pezzo Surface from arXiv Front: math.NT by Daniel Loughran 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.

nLab page on Manin conjecture