Integral Points on a del Pezzo Surface over Imaginary Quadratic Fields

We characterise integral points of bounded log-anticanonical height on a quartic del Pezzo surface of singularity type ${\mathbf{A}}_3$ 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.