Characterization of projective spaces and $\mathbb P^r$-bundles as ample divisors

Jie Liu

Published 2016-11-17Version 1

Let $X$ be a projective manifold of dimension $n$. Suppose that $T_X$ contains an ample subsheaf. We show that $X$ is isomorphic to $\mathbb P^n$. As an application, we derive the classification of projective manifolds containing a $\mathbb P^r$-bundle as an ample divisor by the recent work of D.~Litt.