Integral Points on a del Pezzo Surface over Imaginary Quadratic Fields

2023/07/24 by Ortmann, Judith · 1 citation
#11D45 (Primary) 11G35 #11R11 #14G05 #14J26 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2307.12877

Abstract

We characterise integral points of bounded log-anticanonical height on a quartic del Pezzo surface of singularity type A₃ over imaginary quadratic fields with respect to its singularity and its lines. Furthermore, we count these integral points of bounded height by using universal torsors and interpret the count geometrically to prove an analogue of Manin's conjecture for the set of integral points with respect to the singularity and to a line.

Cited by

• Integral Diophantine approximation on varieties

Related

• Integral points on a del Pezzo surface over imaginary quadratic fields
• Integral points of bounded height on quintic del Pezzo surfaces over number fields
• Counting imaginary quadratic points via universal torsors
• Counting integral points on universal torsors
• Points of bounded height on quintic del Pezzo surfaces over number fields