Extremal Kähler metrics on blow-ups of parabolic ruled surfaces

Details Extremal Kähler metrics on blow-ups of parabolic ruled surfaces Extremal Kähler metrics on blow-ups of parabolic ruled surfaces

2011-04-21

arxiv.org/abs/1104.4315v2

Mathematics

Differential Geometry

43 pages. New exposition of the main results. New presentation of the gluing theory. New section on results about unstable par

Scientific paper

We provide new examples of extremal K\"ahler metrics on blow-ups of parabolic ruled surfaces. The method that we use is based on the gluing construction of Arezzo, Pacard and Singer. This enables us to endow ruled surfaces of the form $\P(\mathcal{O}\oplus L)$ with special parabolic structures such that the associated iterated blow-up admits an extremal metric of non-constant scalar curvature. In particular we find new examples of extremal metrics on blow-ups of unstable parabolic ruled surfaces.

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