Integral Points on Singular Del Pezzo Surfaces

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.

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“…Moreover, the volume is taken on the subset of the adelic points cut out by these automorphic characters. • The formula is compatible with [DW22], treating integral points of several open subvarieties of the minimal desingularization of a singular quartic del Pezzo surface. This variety is an example of a nontoric variety in which the construction of α A does not lead to a simplicial cone.…”