Monomial curves and locally linear resolution
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918154756685824 |
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| author | Hibi, Takayuki Schenzel, Peter |
| author_facet | Hibi, Takayuki Schenzel, Peter |
| contents | For four elements of a Noetherian ring we construct complexes of free modules of length three (resp. five) by an explicit description of the homomorphisms of the free modules. We provide exactness criteria for them. As an application we use these results in order to describe explicit the minimal free resolution of the Hartshorne--Rao module of a monomial curve lying on a smooth quadric. Also it provides an example of linearly generated module with syzygies of arbitrary high degree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04412 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monomial curves and locally linear resolution Hibi, Takayuki Schenzel, Peter Commutative Algebra Primary: 13D02, 13H45, Secondary: 15B99 For four elements of a Noetherian ring we construct complexes of free modules of length three (resp. five) by an explicit description of the homomorphisms of the free modules. We provide exactness criteria for them. As an application we use these results in order to describe explicit the minimal free resolution of the Hartshorne--Rao module of a monomial curve lying on a smooth quadric. Also it provides an example of linearly generated module with syzygies of arbitrary high degree. |
| title | Monomial curves and locally linear resolution |
| topic | Commutative Algebra Primary: 13D02, 13H45, Secondary: 15B99 |
| url | https://arxiv.org/abs/2510.04412 |