K-stability of constant scalar curvature Kähler manifolds

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.

arXiv comment14 pages

References in corpus (4)

• CM Stability and the Generalized Futaki Invariant I
• Extremal metrics and K-stability (PhD thesis)
• Geometry of Kähler Metrics and Foliations by Holomorphic Discs
• Stability of extremal Kähler manifolds

Cited by in corpus (17)

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• A note on the definition of K-stability
• Weighted projective embeddings, stability of orbifolds and constant scalar curvature Kähler metrics
• Extremal Kähler metrics on projective bundles over a curve
• Torus equivariant K-stability
• On the limit of spectral measures associated to a test configuration
• Alpha invariants and K-stability for general polarisations of Fano varieties
• The Kahler-Ricci flow and K-stability
• The K-energy on small deformations of constant scalar curvature Kahler manifolds
• On the uniform K-stability for some asymptotically log del Pezzo surfaces
• Kähler Ricci flow with vanished Futaki invariant
• Emergent complex geometry
• The complex Monge-Ampere equation on compact Kaehler manifolds
• Multiplier ideal sheaves and geometric problems