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On Berman–Gibbs stability and K-stability of
$\mathbb{Q}$-Fano varieties
- Part of
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- Journal:
- Compositio Mathematica / Volume 152 / Issue 2 / February 2016
- Published online by Cambridge University Press:
- 26 November 2015, pp. 288-298
- Print publication:
- February 2016
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- Article
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The notion of Berman–Gibbs stability was originally introduced by Berman for
$\mathbb{Q}$-Fano varieties 
$X$. We show that the pair 
$(X,-K_{X})$ is K-stable (respectively K-semistable) provided that 
$X$ is Berman–Gibbs stable (respectively semistable).
