Monads on projective spaces

Abstract

Let Ε be a vector bundle on P ⁿ. There is a strong relationship between Ε and its intermediate cohomology modules. In the case where Ε has low rank, we exploit this relationship to provide various splitting criteria for Ε. In particular, we give a splitting criterion for Ε in terms of the vanishing of certain intermediate cohomology modules. We also show that the Horrocks-Mumford bundle is the only non-split rank two bundle on P⁴ with a Buchsbaum second cohomology module.