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.

28 pages, 4 figures; improvements in exposition, updated references; appeared in J. Inst. Math. Jussieu

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