Constant scalar curvature Kaehler surfaces and parabolic polystability

Yann Rollin; Michael A. Singer

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arXiv · math/0703212

Constant scalar curvature Kaehler surfaces and parabolic polystability

Yann Rollin·Michael A. Singer

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Abstract

A complex ruled surface admits an iterated blow-up encoded by a parabolic structure with rational weights. Under a condition of parabolic stability, one can construct a Kaehler metric of constant scalar curvature on the blow-up according to math.DG/0412405. We present a generalization of this construction to the case of parabolically polystable ruled surfaces. Thus we can produce numerous examples of Kaehler surfaces of constant scalar curvature with circle or toric symmetry.

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Yann Rollin, Michael A. Singer. 2007-12-04. Constant scalar curvature Kaehler surfaces and parabolic polystability. https://arxiv.org/abs/math/0703212

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