Manin's conjecture on a nonsingular quartic del Pezzo surface

TL;DR

This paper verifies Manin's conjecture regarding the density of rational points on a specific nonsingular quartic del Pezzo surface, confirming the predicted order of magnitude for the number of rational points.

Contribution

It provides a proof that Manin's conjecture holds in order of magnitude for a particular nonsingular quartic del Pezzo surface.

Findings

Confirmed the order of magnitude predicted by Manin's conjecture

Validated the conjecture for a specific quartic del Pezzo surface

Contributed to understanding rational points on algebraic surfaces

Abstract

Given a nonsingular quartic del Pezzo surface, a conjecture of Manin predicts the density of rational points on the open subset of the surface formed by deleting the lines. We prove that this prediction is of the correct order of magnitude for a particular surface.