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# Constant Scalar Curvature Kähler Surfaces and Parabolic Polystability

@inproceedings{ROLLIN2007ConstantSC, title={Constant Scalar Curvature K{\"a}hler Surfaces and Parabolic Polystability}, author={YANN ROLLIN and Michael F. Singer}, year={2007} }

- Published 2007

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 Kähler metric of constant scalar curvature on the blow-up according to [18]. We present a generalization of this construction to the case of parabolically polystable ruled surfaces. Thus we can produce numerous examples of Kähler surfaces of constant scalar curvature with circle or toric symmetry.