Scalar Flat Kähler Metrics on Affine Bundles over CP 1

[摘要] We show that the total space of any affine $\mathbb{C}$-bundle over $\mathbb{CP}^1$ 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.

[关键词] scalar-flat K¨ahler metric;af fine bundle;twistor space