Birational superrigidity and K-stability of Fano complete intersections of index 1

Source abstract

We prove that every smooth Fano complete intersection of index 1 and codimension r in P n + r is birationally superrigid and K-stable if n ≥ 10 r . 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 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.