Mapping free resolutions of length three II -- Module formats
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866911760609443840 |
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| author | Filippini, Sara Angela Guerrieri, Lorenzo |
| author_facet | Filippini, Sara Angela Guerrieri, Lorenzo |
| contents | Let $M$ be a perfect module of projective dimension 3 in a Gorenstein, local or graded ring $R$. We denote by $\FF$ the minimal free resolution of $M$. Using the generic ring associated to the format of $\FF$ we define higher structure maps, according to the theory developed by Weyman in "Generic free resolutions and root systems" (Annales de l'Institut Fourier} 68.3 (2018), pp. 1241--1296). We introduce a generalization of classical linkage for $R$-module using the Buchsbaum--Rim complex, and study the behaviour of structure maps under this Buchsbaum--Rim linkage. In particular, for certain formats we obtain criteria for these $R$-modules to lie in the Buchsbaum--Rim linkage class of a Buchsbaum--Rim complex of length 3. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_10098 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Mapping free resolutions of length three II -- Module formats Filippini, Sara Angela Guerrieri, Lorenzo Commutative Algebra 13D02, 13C05, 13C40 Let $M$ be a perfect module of projective dimension 3 in a Gorenstein, local or graded ring $R$. We denote by $\FF$ the minimal free resolution of $M$. Using the generic ring associated to the format of $\FF$ we define higher structure maps, according to the theory developed by Weyman in "Generic free resolutions and root systems" (Annales de l'Institut Fourier} 68.3 (2018), pp. 1241--1296). We introduce a generalization of classical linkage for $R$-module using the Buchsbaum--Rim complex, and study the behaviour of structure maps under this Buchsbaum--Rim linkage. In particular, for certain formats we obtain criteria for these $R$-modules to lie in the Buchsbaum--Rim linkage class of a Buchsbaum--Rim complex of length 3. |
| title | Mapping free resolutions of length three II -- Module formats |
| topic | Commutative Algebra 13D02, 13C05, 13C40 |
| url | https://arxiv.org/abs/2303.10098 |