We prove that every birationally superrigid Fano variety whose alpha invariant is greater than (resp. no smaller than) 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 1/n+1 (under mild assumptions) and that the moduli space (if exists) of birationally superrigid Fano varieties is separated.
|Original language||English (US)|
|State||Published - Feb 22 2018|
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