Relative K-polystability of projective bundles over a curve

Vestislav Apostolov; Julien Keller

Relative K-polystability of projective bundles over a curve

Algebraic Geometry 2017-02-13 v2 Complex Variables Differential Geometry

Authors: Vestislav Apostolov , Julien Keller

Abstract

Let $P(E)$ be the projectivization of a holomorphic vector bundle $E$ over a compact complex curve $C$ . We characterize the existence of an extremal K\"ahler metric on the ruled manifold $P(E)$ in terms of relative K-polystability and the fact that $E$ decomposes as a direct sum of stable bundles.

Keywords

relative K-polystability projective bundle holomorphic vector bundle extremal Kähler metric ruled manifold stable bundle

Cite

@article{arxiv.1701.08507,
  title  = {Relative K-polystability of projective bundles over a curve},
  author = {Vestislav Apostolov and Julien Keller},
  journal= {arXiv preprint arXiv:1701.08507},
  year   = {2017}
}

Comments

32 pages. References updated

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