K-stability of Log Fano Cone Singularities

Abstract: We generalize the valuative criterion for K-stability of Fano varieties to log Fano cone singularities. We also show the higher rank finite generation conjecture for log Fano cone singularities, which implies the Yau-Tian-Donaldson Conjecture for Sasakian-Einstein metric.

algebraic geometry

Audience: researchers in the topic

Algebraic Geometry NorthEastern Series (AGNES)