Alpha invariant and K-stability of Q-Fano varieties

摘要

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