Nobuhiro Honda, “Scalar Flat Kähler Metrics on Affine Bundles over <nobr>$\mathbb{CP}^1$</nobr>”, SIGMA, 2014, Volume 10,046, 25 pp.

This article is cited in 4 papers

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

Nobuhiro Honda

Mathematical Institute, Tohoku University, Sendai, Miyagi, Japan

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.

Keywords: scalar-flat Kähler metric; affine bundle; twistor space.

MSC: 53A30

Received: November 12, 2013; in final form April 15, 2014; Published online April 19, 2014

Language: English

DOI: 10.3842/SIGMA.2014.046