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Constant Scalar Curvature Kahler Surfaces and Parabolic Polystability

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


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.

    Research areas

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

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