Birational superrigidity and K-stability of Fano complete intersections of index one (with an appendix written jointly with Charlie Stibitz)

Abstract

We prove that every smooth Fano complete intersection of index $1$ and codimension $r$ in ${\mathbb{P}}^{n+r}$ is birationally superrigid and K-stable if $n\ge 10r$. We also propose a generalization of Tian's criterion of K-stability and, as an application, prove the K-stability of the complete intersection of a quadric and a cubic in ${\mathbb{P}}^5$. In the appendix (written jointly with C. Stibitz), we prove the conditional birational superrigidity of Fano complete intersections of higher index in large dimension.

18 pages. Final version

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Cited by in corpus (8)

• 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
• Birationally rigid complete intersections of high codimension
• K-stability of birationally superrigid Fano 3-fold weighted hypersurfaces
• Seshadri constants and K-stability of Fano manifolds
• Alpha invariants of birationally bi-rigid Fano 3-folds I
• Symmetries of Fano varieties
• On K-stability of Fano weighted hypersurfaces