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K-STABILITY OF FANO MANIFOLDS WITH NOT SMALL ALPHA INVARIANTS

Published online by Cambridge University Press:  30 March 2017

Kento Fujita*
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan ([email protected])

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.

Type
Research Article
Copyright
© Cambridge University Press 2017 

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