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 $1$.

119 pages. Final version

References in corpus (1)

• Alpha invariants of birationally bi-rigid Fano 3-folds I

Cited by in corpus (1)

• On K-stability of Fano weighted hypersurfaces