English

K-stability and parabolic stability

Differential Geometry 2013-04-02 v3

Abstract

Parabolic structures with rational weights encode certain iterated blowups of geometrically ruled surfaces. In this paper, we show that the three notions of parabolic polystability, K-polystability and existence of constant scalar curvature K\"ahler metrics on the iterated blowup are equivalent, for certain polarizations close to the boundary of the K\"ahler cone.

Keywords

Cite

@article{arxiv.1303.2332,
  title  = {K-stability and parabolic stability},
  author = {Yann Rollin},
  journal= {arXiv preprint arXiv:1303.2332},
  year   = {2013}
}

Comments

20 pages. Many typos corrected in this version

R2 v1 2026-06-21T23:39:33.312Z