Syzygy Theoretic Approach to Horrocks-type Criteria for Vector Bundles

Abstract

This paper studies a variant of Horrocks-type criteria for vector bundles mainly through a syzygy theoretic approach. Starting with explaining various proofs of the splitting criteria for ACM and Buchsbaum bundles, we are going to give new sights of an investigation of quasi-Buchsbaum bundles. Not only our result characterizes the null-correlation bundle on ${\mathbb P}^n$, but also our approach classifies quasi-Buchsbaum bundles on ${\mathbb P}^3$ with simple cohomologies in terms of standard system of parameters and the corresponding skew-symmetric matrices towards a study of the structure of quasi-Buchsbaum modules.