Birational superrigidity and K-stability of projectively normal Fano manifolds of index one

Abstract

We prove that every projectively normal Fano manifold in ${\mathbb{P}}^{n+r}$ of index $1$, codimension $r$ and dimension $n\ge 10r$ is birationally superrigid and K-stable. This result was previously proved by Zhuang under the complete intersection assumption.

11 pages, comments are welcome, v2. the exposition is improved; to appear in Michigan Mathematical Journal

References in corpus (1)

• Birationally rigid complete intersections of quadrics and cubics