K-stability of birationally superrigid Fano 3-fold weighted hypersurfaces

Abstract

We prove that the alpha invariant of a quasi-smooth Fano 3-fold weighted hypersurface of index $1$ is greater than or equal to $1/2$. Combining this with the result of Stibitz and Zhuang \cite{SZ19} on a relation between birational superrigidity and K-stability, we prove the K-stability of a birationally superrigid quasi-smooth Fano 3-fold weighted hypersurfaces of index $1$.

arXiv comment119 pages. Final version

References in corpus (7)

• Fano 3-folds in codimension 4, Tom and Jerry, Part I
• Birationally rigid Fano threefold hypersurfaces
• Birational superrigidity and K-stability of Fano complete intersections of index one (with an appendix written jointly with Charlie Stibitz)
• Birational superrigidity and K-stability of singular Fano complete intersections
• Birational Mori fiber structures of Q-Fano 3-fold weighted complete intersections, II
• Birational superrigidity is not a locally closed property
• Alpha invariants of birationally bi-rigid Fano 3-folds I

Cited by in corpus (1)

• On K-stability of Fano weighted hypersurfaces