Manin's conjecture for quintic del Pezzo surfaces with a conic bundle structure

TL;DR

This paper studies Manin's conjecture for degree five del Pezzo surfaces with a conic bundle, establishing bounds and confirming the conjecture in the Galois general case.

Contribution

It provides the first proof of Manin's conjecture for this class of surfaces, including the Galois general case.

Findings

Established matching upper and lower bounds.

Confirmed Manin's conjecture in the Galois general case.

Advances understanding of rational points on del Pezzo surfaces.

Abstract

We investigate Manin's conjecture for del Pezzo surfaces of degree five with a conic bundle structure, proving matching upper and lower bounds, and the full conjecture in the Galois general case.