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arXiv · 1606.08261

K-stability of Fano manifolds with not small alpha invariants

Kento Fujita
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Abstract

We show that any $n$-dimensional Fano manifold $X$ with $\alpha(X)=n/(n+1)$ and $n\geq 2$ is K-stable, where $\alpha(X)$ is the alpha invariant of $X$ introduced by Tian. In particular, any such $X$ admits K\"ahler-Einstein metrics and the holomorphic automorphism group of $X$ is finite.

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Kento Fujita. 2016-06-27. K-stability of Fano manifolds with not small alpha invariants. https://arxiv.org/abs/1606.08261

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