Alpha invariant and K-stability of Q-Fano varieties

Details Alpha invariant and K-stability of Q-Fano varieties Alpha invariant and K-stability of Q-Fano varieties

2010-11-29

arxiv.org/abs/1011.6131v1

Mathematics

Algebraic Geometry

17 pages

Scientific paper

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.

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