Alpha invariant and K-stability of Q-Fano varieties
classification
🧮 math.AG
math.DG
keywords
alpha-invariantk-stabilityproofq-fanoalgebro-geometricalphaapplicationsautomorphism
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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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