English

Constant scalar curvature Kaehler surfaces and parabolic polystability

Differential Geometry 2007-12-04 v2 Algebraic Geometry

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 Kaehler metric of constant scalar curvature on the blow-up according to math.DG/0412405. We present a generalization of this construction to the case of parabolically polystable ruled surfaces. Thus we can produce numerous examples of Kaehler surfaces of constant scalar curvature with circle or toric symmetry.

Keywords

Cite

@article{arxiv.math/0703212,
  title  = {Constant scalar curvature Kaehler surfaces and parabolic polystability},
  author = {Yann Rollin and Michael A. Singer},
  journal= {arXiv preprint arXiv:math/0703212},
  year   = {2007}
}

Comments

28 pages; no figures; v2 relaxed notion of sporadic parabolic structures

R2 v1 2026-07-22T17:52:19.812Z