K-stability of birationally superrigid Fano varieties

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.

arXiv comment7 pages. Comments welcome

References in corpus (5)

• K-semistability is equivariant volume minimization
• On the proper moduli spaces of smoothable Kähler-Einstein Fano varieties
• Uniform K-stability and plt blowups of log Fano pairs
• Erratum to: Birationally rigid hypersurfaces
• Deformations of canonical pairs and Fano varieties

Cited by in corpus (4)

• Birational superrigidity and K-stability of singular Fano complete intersections
• Birational superrigidity and K-stability of Fano complete intersections of index one (with an appendix written jointly with Charlie Stibitz)
• Birational superrigidity is not a locally closed property
• Higher Codimensional Alpha Invariants and Characterization of Projective Spaces