Alpha invariant and K-stability of Q-Fano varieties

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  • Alpha invariant and K-stability of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="double-struck">Q</mml:mi></mml:math>-Fano varieties

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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.

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