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On Berman–Gibbs stability and K-stability of $\mathbb{Q}$-Fano varieties

Part of: Algebraic groups Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  26 November 2015

Kento Fujita
Kento Fujita*
Affiliation:
Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan email fujita@math.kyoto-u.ac.jp
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Abstract

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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).

Keywords

Fano varietiesK-stabilitymultiplier ideal sheavesKähler–Einstein metrics

MSC classification

Primary: 14L24: Geometric invariant theory
Secondary: 14J17: Singularities
Type
Research Article
Information
Compositio Mathematica , Volume 152 , Issue 2 , February 2016 , pp. 288 - 298
Copyright
© The Author 2015 

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