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.

arXiv comment28 pages, 4 figures; improvements in exposition, updated references; appeared in J. Inst. Math. Jussieu

References in corpus (6)

• Singular del Pezzo surfaces whose universal torsors are hypersurfaces
• Tamagawa numbers of polarized algebraic varieties
• Integral points of bounded height on partial equivariant compactifications of vector groups
• Integral points of bounded height on toric varieties
• Cox rings over nonclosed fields
• Integral points of bounded height on a log Fano threefold

Cited by in corpus (1)

• Integral points of bounded height on a certain toric variety