Syzygy Theoretic Approach to Horrocks-type Criteria for Vector Bundles

This paper studies a variant of Horrocks-type criteria for vector bundles mainly through a syzygy theoretic approach.

Starting with sketching splitting criteria for ACM and Buchsbaum bundles on projective space, we try to give new sights of an investigation of quasi-Buchsbaum bundles.

Not only our result characterizes the null-correlation bundle on P^n, but also classifies vector bundles on P^3 with simple intermediate cohomologies in terms of standard system of parameters and the corresponding skew-symmetric matrices.

Our approach leads to an extended study of quasi-Buchsbaum bundles on P^n with small intermediate cohomologies.