Degenerations of LeBrun twistor spaces

Details Degenerations of LeBrun twistor spaces Degenerations of LeBrun twistor spaces

2010-01-20

arxiv.org/abs/1001.3461v3

Mathematics

Differential Geometry

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

Scientific paper

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.

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