Globally generated vector bundles with small c1 on projective spaces - volume 253, number 1209

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 $n \leq 5$.