BIRATIONAL SUPERRIGIDITY AND K-STABILITY OF FANO COMPLETE INTERSECTIONS OF INDEX 1

摘要

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 ≥ 10r. We also propose a generalization of Tian’s criterion of K-stability and, as an application, prove the Kstability 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.