Globally generated vector bundles with small c1 on projective spaces, II

We complete the classification of globally generated vector bundles with c1≤5$c_1 \le 5$ on projective spaces by treating the case c1=5$c_1 = 5$ on Pn$\mathbb {P}^n$, n≥4$n \ge 4$. It turns out that there are very few indecomposable bundles of this kind: besides some obvious examples there are, roughly speaking, only the (first twist of the) rank 5 vector bundle which is the middle term of the monad defining the Horrocks bundle of rank 3 on P5$\mathbb {P}^5$, and its restriction to P4$\mathbb {P}^4$. We recall, in an appendix, from one of our previous papers, the main results allowing the classification of globally generated vector bundles with c1=5$c_1 = 5$ on P3$\mathbb {P}^3$. Since there are many such bundles, a large part of the main body of the paper is occupied with the proof of the fact that, except for the simplest ones, they do not extend to P4$\mathbb {P}^4$ as globally generated vector bundles.