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 -bundle over 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}
}