Alpha invariant and K-stability of Q-Fano varieties

Abstract

We give a purely algebro-geometric proof that if the alpha-invariant of a Q-Fano variety X is greater than dim X/(dim X+1), then (X,O(-K_X)) is K-stable. The key of our proof is a relation among the Seshadri constants, the alpha-invariant and K-stability. It also gives applications concerning the automorphism group.

Final version (published)

References in corpus (6)

• K-stability of constant scalar curvature polarization
• Special test configurations and $K$-stability of Fano varieties
• A stronger concept of K-stability
• Log canonical thresholds of certain Fano hypersurfaces
• A note on the definition of K-stability
• The Calabi conjecture and K-stability

Cited by in corpus (6)

• Stable Pairs and Coercive Estimates for The Mabuchi Functional
• Testing log K-stability by blowing up formalism
• On K-stability of some del Pezzo surfaces of Fano index 2
• Alpha-invariant of Toric Line Bundles
• Log canonical thresholds of Del Pezzo Surfaces in characteristic p
• Birational superrigidity and slope stability of Fano manifolds