On uniform log $K$-stability for constant scalar curvature Kähler cone metrics

Abstract

We prove that the existence of constant scalar curvature Kähler metrics with cone singularities along a divisor implies log $K$-polystability and $G$-uniform log $K$-stability, where $G$ is the automorphism group which preserves the divisor. We also show that a constant scalar curvature Kähler cone metric along an ample divisor of sufficiently large degree always exists. We further show several properties of the path of constant scalar curvature Kähler cone metrics and discuss uniform log $K$-stability of normal varieties.

58 pages

Cited by in corpus (1)

• Existence of constant scalar curvature Kaehler cone metrics, properness and geodesic stability