Journal of Geometric Analysis

, Volume 19, Issue 1, pp 107–136 | Cite as

Constant Scalar Curvature Kähler Surfaces and Parabolic Polystability

  • Yann RollinEmail author
  • Michael Singer


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 Rollin and Singer (J. Eur. Math. Soc., 2004). 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.


Kähler Constant scalar curvature Ruled surfaces Stability 

Mathematics Subject Classification (2000)

53C25 32Q20 


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Copyright information

© Mathematica Josephina, Inc. 2008

Authors and Affiliations

  1. 1.Imperial CollegeLondonUK
  2. 2.University of EdinburghEdinburghUK

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