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 $\mathbb{Q}$-divisors. First, we propose a condition in terms of certain anti-canonical $\mathbb{Q}$-divisors of given Fano variety, which we conjecture to be equivalent to the K-stability. We prove that it is at least a sufficient condition and also related 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.
Citation
Kento Fujita. Yuji Odaka. "On the K-stability of Fano varieties and anticanonical divisors." Tohoku Math. J. (2) 70 (4) 511 - 521, 2018. https://doi.org/10.2748/tmj/1546570823
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