  We show that the total space of any affine $\mathbb{C}$-bundle over
$\mathbb{CP}^1$ with negative degree admits an ALE scalar-flat K\"ahler 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.

Differential Geometry