Constant Scalar Curvature Kahler Surfaces and Parabolic Polystability

Yann Rollin, Michael Singer

Research output: Contribution to journalArticlepeer-review

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 Kahler 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 Kahler surfaces of constant scalar curvature with circle or toric symmetry.

Original languageEnglish
Pages (from-to)107-136
Number of pages30
JournalJournal of Geometric Analysis
Volume19
Issue number1
DOIs
Publication statusPublished - Jan 2009

Keywords

  • Kahler
  • Constant scalar curvature
  • Ruled surfaces
  • Stability
  • 53C25
  • 32Q20
  • DEFORMATION-THEORY
  • VECTOR-BUNDLES
  • METRICS
  • STABILITY

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