Surveys in Differential Geometry

Volume 19 (2014)

Algebraic families of constant scalar curvature Kähler metrics

Pages: 111 – 137



Simon Donaldson (Department of Pure Mathematics, Imperial College, London, United Kingdom)


We give a new proof of the fact that the condition of a Fano manifold admitting a Kähler-Einstein metric is Zariski-open (provided that the automorphism group is discrete). This proof does not use the characterisation involving stability. The arguments involve estimates of Futaki invariants obtained from a differential-geometric “volume estimate” and variants of the algebro-geometric arguments of Stoppa. Many of the ideas apply to constant scalar curvature Kähler metrics.

2010 Mathematics Subject Classification


Published 6 March 2015