Algebraic families of constant scalar curvature Kähler metrics

2015/03/17 by Donaldson, Simon · 1 citation
#53C55 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1503.05174

Abstract

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.

Cited by

• On the Bergman kernel of polarized abelian varieties

Related

• Kähler-Einstein metrics along the smooth continuity method
• Microscopic stability thresholds and constant scalar curvature Kähler metrics
• Kahler-Einstein metrics and stability
• On the existence of Kähler metrics of constant scalar curvature
• Symmetries, Quotients and Kaehler-Einstein metrics