Abstract

Horrocks' criterion says that a vector bundle on a complex projective space of dimension at least 3 splits as a direct sum of line bundles if and only if its restriction to a hyperplane splits. We generalize this criterion to a class of varieties of dimension at least 4, which includes multiprojective spaces, Grassmannians, and global complete intersections. Our main tools are the Grothendieck-Lefschetz theorem on Picard groups and Zariski sheaf cohomology.



Information: