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arXiv · 1903.04719

On the sharpness of Tian's criterion for K-stability

Yuchen Liu·Ziquan Zhuang
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Abstract

Tian's criterion for K-stability states that a Fano variety of dimension $n$ whose alpha invariant is greater than $\frac{n}{n+1}$ is K-stable. We show that this criterion is sharp by constructing singular Fano varieties with alpha invariants $\frac{n}{n+1}$ that are not K-polystable for sufficiently large $n$. We also construct K-unstable Fano varieties with alpha invariants $\frac{n-1}{n}$.

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Yuchen Liu, Ziquan Zhuang. 2019-03-12. On the sharpness of Tian's criterion for K-stability. https://arxiv.org/abs/1903.04719

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