Abstract
Let ℰ be a vector bundle on Pn. There is a strong relationship between ℰ and its intermediate cohomology modules. In the case where ℰ has low rank, we exploit this relationship to provide various splitting criteria for ℰ. In particular, we give a splitting criterion for ℰ 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.
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