Globally Generated Vector Bundles With Small C 1 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 �� 5 one the projective plane and with c1 �� 4 on the projective n-space for n �� 3. This reproves and extends, in a systematic manner, previous results obtained for c1 �� 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 �� n ? 1 on the projective n-space. They verify the conjecture for n �� 5.

2018 | ISBN-10: 1470428385