Birational Superrigidity and K-Stability of Projectively Normal Fano Manifolds of Index One

Abstract

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