Syzygy Theoretic Approach to Horrocks-type Criteria for Vector Bundles
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912579954147328 |
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| author | Miyazaki, Chikashi |
| author_facet | Miyazaki, Chikashi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17625 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Syzygy Theoretic Approach to Horrocks-type Criteria for Vector Bundles Miyazaki, Chikashi Algebraic Geometry 13H10, 14F05, 14J60 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. |
| title | Syzygy Theoretic Approach to Horrocks-type Criteria for Vector Bundles |
| topic | Algebraic Geometry 13H10, 14F05, 14J60 |
| url | https://arxiv.org/abs/2403.17625 |