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arXiv · 1802.08381

K-stability of birationally superrigid Fano varieties

Charlie Stibitz·Ziquan Zhuang
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Abstract

We prove that every birationally superrigid Fano variety whose alpha invariant is greater than (resp. no smaller than) $\frac{1}{2}$ is K-stable (resp. K-semistable). We also prove that the alpha invariant of a birationally superrigid Fano variety of dimension $n$ is at least $\frac{1}{n+1}$ (under mild assumptions) and that the moduli space (if exists) of birationally superrigid Fano varieties is separated.

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Charlie Stibitz, Ziquan Zhuang. 2018-02-23. K-stability of birationally superrigid Fano varieties. https://doi.org/10.1112/s0010437x19007498

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