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K-stability of birationally superrigid Fano varieties
Part of
Charlie Stibitz, Ziquan Zhuang
Journal:

Compositio Mathematica / Volume 155 / Issue 9 / September 2019

Published online by Cambridge University Press:

07 August 2019, pp. 1845-1852

Print publication:

September 2019
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We prove that every birationally superrigid Fano variety whose alpha invariant is greater than (respectively no smaller than) $\frac{1}{2}$ is K-stable (respectively K-semistable). We also prove that the alpha invariant of a birationally superrigid Fano variety of dimension $n$ is at least $1/(n+1)$ (under mild assumptions) and that the moduli space (if it exists) of birationally superrigid Fano varieties is separated.