Some remarks on Buchsbaum bundles

Let E be a vector bundle on . We say E is Buchsbaum if Hp(EM(*)) has trivial module structure for each linear space M and for all 1≤p≤dimM−1. In this note, we show that a Buchsbaum bundle is either an Ω-bundle (i.e. a direct sum of Ωp(h)ʹs, where Ωp is the pth exterior power of the contangent bundle of ) or the quotient of an Ω-bundle by a direct sum of line bundles. We also give a strategy to characterize/construct Buchsbaum bundles, give conditions for an Ω-bundle to be extendable.