SC - 1093 | Globally Generated Vector Bundles With Small c1 on Projective Spaces

Globally Generated Vector Bundles With Small C 1 on Projective Spaces by Cristian Anghel (Author), Iustin Coanda (Author), Nicolae Manolache (Author)

The authors provide a complete classification of globally generated vector bundles with first Chern class $c1 leq 5$ one the projective plane and with $c1 leq 4$ on the projective $n$-space for $n geq 3$. This reproves and extends, in a systematic manner, previous results obtained for $c1 leq 2$ by Sierra and Ugaglia [J. Pure Appl. Algebra 213 (2009), 2141-2146], and for $c1 = 3$ 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 $c1 = 4$ 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 $c1 leq n - 1$ on the projective $n$-space. They verify the conjecture for $n leq 5$.

2018 | ISBN-10: 1470428385 | ID: SC - 1093