English

Deformation of LeBrun's ALE metrics with negative mass

Differential Geometry 2015-06-04 v3

Abstract

In this article we investigate deformations of a scalar-flat K\"ahler metric on the total space of complex line bundles over CP^1 constructed by C. LeBrun. In particular, we find that the metric is included in a one-dimensional family of such metrics on the four-manifold, where the complex structure in the deformation is not the standard one.

Keywords

Cite

@article{arxiv.1204.4857,
  title  = {Deformation of LeBrun's ALE metrics with negative mass},
  author = {Nobuhiro Honda},
  journal= {arXiv preprint arXiv:1204.4857},
  year   = {2015}
}

Comments

20 pages, no figure. V2: added two references, filled a gap in the proof of Theorem 1.2. V3: corrected a wrong statement about Kuranishi family of a Hirzebruch surface stated in the last paragraph in the proof of Theorem 1.2, and fixed a relevant error in the proof. Also added a reference [24] about Kuranishi family of Hirzebruch surfaces