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arXiv · 1011.6131

Alpha invariant and K-stability of Q-Fano varieties

Yuji Odaka·Yuji Sano
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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.

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Yuji Odaka, Yuji Sano. 2010-11-29. Alpha invariant and K-stability of Q-Fano varieties. https://arxiv.org/abs/1011.6131

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