Scalar Flat Kähler Metrics on Affine Bundles over ${\mathbb{CP}}^1$

Abstract

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.

References in corpus (1)

• Einstein metrics and complex singularities

Cited by in corpus (1)

• Invariant scalar-flat Kähler metrics on line bundles over generalized flag varieties