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arXiv · 1602.01305

On the K-stability of Fano varieties and anticanonical divisors

Kento Fujita·Yuji Odaka
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Abstract

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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Kento Fujita, Yuji Odaka. 2016-02-03. On the K-stability of Fano varieties and anticanonical divisors. https://arxiv.org/abs/1602.01305

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