Constant Scalar Curvature Kähler Surfaces and Parabolic Polystability

  title={Constant Scalar Curvature K{\"a}hler Surfaces and Parabolic Polystability},
  author={YANN ROLLIN and Michael F. 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 [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. 

From This Paper

Topics from this paper.


Publications citing this paper.
Showing 1-2 of 2 extracted citations


Publications referenced by this paper.
Showing 1-10 of 18 references

Notes on git and symplectic reduction for bundles and varieties

  • R. P. Thomas.
  • 2006

Non - minimal scalarflat Kähler surfaces and parabolic stability

  • M. Singer.
  • Invent . Math .
  • 2005

Construction of Kähler surfaces with constant scalar curvature

  • M. Singer.
  • Jour . of the Eur . Math . Soc .
  • 2004

Métriques kählériennes à courbure scalaire constante : unicité

  • O. Biquard.
  • Astérisque , pages Exp . No .
  • 2004

Compact manifolds with special holonomy

  • C. LeBrun J. Kim, M. Pontecorvo
  • Oxford Mathematical Monographs
  • 2000

Similar Papers

Loading similar papers…