Extremal K\"ahler metrics on blow-ups of parabolic ruled surfaces
classification
🧮 math.DG
keywords
extremalparabolicruledsurfacesahlerblow-upsmetricsadmits
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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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