Globally generated vector bundles with small

The authors provide a complete classification of globally generated vector bundles with first Chern class c_1 \leq 5 one the projective plane and with c_1 \leq 4 on the projective n-space for n \geq 3. This reproves and extends, in a systematic manner, previous results obtained for c_1 \leq 2 by Sierra and Ugaglia [J. Pure Appl. Algebra 213 (2009), 2141-2146], and for c_1 = 3 by Anghel and Manolache [Math. Nachr. 286 (2013), 1407-1423] and, independently, by Sierra and Ugaglia [J. Pure Appl. Algebra 218 (2014), 174-180]. It turns out that the case c_1 = 4 is much more involved than the previous cases, especially on the projective 3-space. Among the bundles appearing in our classification one can find the Sasakura rank 3 vector bundle on the projective 4-space (conveniently twisted). The authors also propose a conjecture concerning the classification of globally generated vector bundles with c_1 \leq n - 1 on the projective n-space. They verify the conjecture for n \leq 5.