A note on the definition of K-stability

Abstract

As recently pointed out by Li and Xu, the definition of K-stability, and the author's proof of K-stability for cscK manifolds without holomorphic vector fields, need to be altered slightly: the Donaldson-Futaki invariant is positive for all test configurations which are not trivial in codimension 2.

2 pages

References in corpus (3)

• Special test configurations and $K$-stability of Fano varieties
• K-stability of constant scalar curvature Kähler manifolds
• Filtrations and test-configurations

Cited by in corpus (7)

• Torus equivariant K-stability
• Scalar curvature and Futaki invariant of Kähler metrics with cone singularities along a divisor
• Openness results for uniform K-stability
• Alpha invariants and K-stability for general polarisations of Fano varieties
• On parametrization, optimization and triviality of test configurations
• Minimizing CM degree and slope stability of projective varieties
• On the continuity of Weil-Petersson volumes of the moduli space weighted points on the projective line