English

Degenerations of LeBrun twistor spaces

Differential Geometry 2015-05-18 v3

Abstract

We investigate various limits of the twistor spaces associated to the self-dual metrics on n CP ^2, the connected sum of the complex projective planes, constructed by C. LeBrun. In particular, we explicitly present the following 3 kinds of degenerations whose limits of the metrics are: (a) LeBrun metrics on (n-1) CP ^2$, (b) (Another) LeBrun metrics on the total space of the line bundle O(-n) over CP ^1 (c) The hyper-Kaehler metrics on the small resolution of rational double points of type A_{n-1}, constructed by Gibbons and Hawking.

Keywords

Cite

@article{arxiv.1001.3461,
  title  = {Degenerations of LeBrun twistor spaces},
  author = {Nobuhiro Honda},
  journal= {arXiv preprint arXiv:1001.3461},
  year   = {2015}
}

Comments

21 pages, 7 figures. V2: A new section added at the end of the article. V3: Reference slightly updated