Integral points on singular del Pezzo surfaces

TL;DR

This paper classifies weak del Pezzo pairs and proves an analogue of Manin's conjecture for integral points on a specific singular quartic del Pezzo surface, advancing understanding of rational points on algebraic surfaces.

Contribution

It introduces a classification of weak del Pezzo pairs and establishes a Manin-type conjecture for integral points on a singular quartic del Pezzo surface.

Findings

Classification of weak del Pezzo pairs.

Proof of Manin's conjecture analogue for a specific surface.

Insights into integral points related to singularities and lines.

Abstract

In order to study integral points of bounded log-anticanonical height on weak del Pezzo surfaces, we classify weak del Pezzo pairs. As a representative example, we consider a quartic del Pezzo surface of singularity type $\mathbf{A}_1+\mathbf{A}_3$ and prove an analogue of Manin's conjecture for integral points with respect to its singularities and its lines.