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K-STABILITY OF FANO MANIFOLDS WITH NOT SMALL ALPHA INVARIANTS

Part of: Surfaces and higher-dimensional varieties Algebraic groups

Published online by Cambridge University Press:  30 March 2017

Kento Fujita
Kento Fujita*
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan (fujita@kurims.kyoto-u.ac.jp)
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Abstract

We show that any $n$-dimensional Fano manifold $X$ with $\unicode[STIX]{x1D6FC}(X)=n/(n+1)$ and $n\geqslant 2$ is K-stable, where $\unicode[STIX]{x1D6FC}(X)$ is the alpha invariant of $X$ introduced by Tian. In particular, any such $X$ admits Kähler–Einstein metrics and the holomorphic automorphism group $\operatorname{Aut}(X)$ of $X$ is finite.

Keywords

Fano varietiesK-stabilityKähler–Einstein metrics

MSC classification

Primary: 14J45: Fano varieties
Secondary: 14L24: Geometric invariant theory
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 18 , Issue 3 , May 2019 , pp. 519 - 530
Copyright
© Cambridge University Press 2017 

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