Scalar Flat Kähler Metrics on Affine Bundles over CP¹ - Honda, N. (Symmetry, Integrability and Geometry: Methods and Applications, 2014)
We show that the total space of any affine C-bundle over CP¹ with negative degree admits an ALE scalar-flat Kähler metric. Here the degree of an affine bundle means the negative of the self-intersection number of the section at infinity in a natural compactification of the bundle, and so for line bundles it agrees with the usual notion of the degree.