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arXiv · 1104.4315

Extremal K\"ahler metrics on blow-ups of parabolic ruled surfaces

Carl Tipler
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Abstract

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

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Carl Tipler. 2011-04-21. Extremal K\"ahler metrics on blow-ups of parabolic ruled surfaces. https://arxiv.org/abs/1104.4315

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