Let $\mathcal F$ be an ample subsheaf of $T_{\mathbb P^n}$. Is it actually locally free? If not, is there a counterexample?
1 Answer
$\begingroup$
$\endgroup$
Yes, $\mathcal{F}$ is locally free. See e.g. Corollary A.11 in this paper of Aprodu, Kebekus, and Peternell.