Journal
TOHOKU MATHEMATICAL JOURNAL
Volume 70, Issue 4, Pages 511-521Publisher
TOHOKU UNIVERSITY
DOI: 10.2748/tmj/1546570823
Keywords
Fano varieties; K-stability; Kahler-Einstein metrics
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Funding
- JSPS Fellowship for Young Scientists
- JSPS Kakenhi [30700356]
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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 anti-canonical 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.
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