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On the K-stability of Fano varieties and anticanonical divisors

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arxiv 1602.01305 v2 pith:YCZ2BGED submitted 2016-02-03 math.AG math.DG

On the K-stability of Fano varieties and anticanonical divisors

classification math.AG math.DG
keywords fanok-stabilityanticanonicalconditionvarietiesfirstgiveq-divisors
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We apply a recent theorem of Li and the first author to give some criteria for the K-stability of Fano varieties in terms of anticanonical Q-divisors. First, we propose a condition in terms of certain anticanonical Q-divisors of given Fano variety, which we conjecture to be equivalent to the K-stability. We prove that it is at least sufficient condition and also relate to the Berman-Gibbs stability. We also give another algebraic proof of the K-stability of Fano varieties which satisfy Tian's alpha invariants condition.

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