English

Scalar Flat K\"ahler Metrics on Affine Bundles over $\mathbb{CP}^1$

Differential Geometry 2014-04-22 v2

Abstract

We show that the total space of any affine C\mathbb{C}-bundle over CP1\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.

Keywords

Cite

@article{arxiv.1311.2391,
  title  = {Scalar Flat K\"ahler Metrics on Affine Bundles over $\mathbb{CP}^1$},
  author = {Nobuhiro Honda},
  journal= {arXiv preprint arXiv:1311.2391},
  year   = {2014}
}