Curvature of scalar-flat Kähler metrics on non-compact symplectic toric 4-manifolds

In this paper, we show that the complete scalar-flat Kähler metrics constructed in [4] on strictly unbounded toric 4-dimensional orbifolds have finite L2 norm of the full Riemannian tensor. In particular, this answers a question of Donaldson's from [12] on the corresponding Generalized Taub-NUT metric on R4. This norm is explicitly determined when the underlying toric manifold is the minimal resolution of a cyclic singularity of the form C2/Zk. In the Ricci-flat case corresponding to gravitational instantons, this recovers a recent result in [5].