K-stability of constant scalar curvature Kähler manifolds

doi:10.1016/j.aim.2009.02.013

Advances in Mathematics

Volume 221, Issue 4, 10 July 2009, Pages 1397-1408

https://doi.org/10.1016/j.aim.2009.02.013 Get rights and content

Under an Elsevier user license

open archive

Abstract

We show that a polarised manifold with a constant scalar curvature Kähler metric and discrete automorphisms is K-stable. This refines the K-semistability proved by S.K. Donaldson.

MSC

53C55

14L24

Keywords

Canonical metrics in Kähler geometry

Stability in algebraic geometry