Splitting criteria for vector bundles on higher dimensional varieties

Abstract

We generalize Horrocks' criterion for the splitting of vector bundles on projective space. We establish an analogous splitting criterion for vector bundles on a class of smooth complex projective varieties of dimension at least four, over which every extension of line bundles splits.

final version: Horrocks scheme defined, more references added, 10 pages, to appear in Pacific J. Math

References in corpus (2)

• A splitting criterion for rank 2 vector bundles on hypersurfaces in P^4
• A splitting criterion for vector bundles on blowing ups of the plane