Syzygy Theoretic Approach to Horrocks-type Criteria for Vector Bundles

Chikashi Miyazaki

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arXiv · 2403.17625

Syzygy Theoretic Approach to Horrocks-type Criteria for Vector Bundles

Chikashi Miyazaki

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Abstract

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.

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Chikashi Miyazaki. 2024-03-26. Syzygy Theoretic Approach to Horrocks-type Criteria for Vector Bundles. https://arxiv.org/abs/2403.17625

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