Linear quotients, linear resolutions and the lcm-lattice
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914135164321792 |
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| author | Varshavsky, Roni |
| author_facet | Varshavsky, Roni |
| contents | Linear resolutions and the stronger notion of linear quotients are important properties of monomial ideals. In this paper, we fully characterize linear quotients in terms of the lcm-lattice of monomial ideals. We also formulate an analogous characterization for monomial ideals with linear resolutions, making explicit a relationship that is implicit in the existing literature. These results complement characterizations of these two properties in terms of the Alexander dual of the corresponding Stanley-Reisner simplicial complex. In addition, we discuss applications to the case of edge ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23520 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear quotients, linear resolutions and the lcm-lattice Varshavsky, Roni Commutative Algebra Combinatorics Linear resolutions and the stronger notion of linear quotients are important properties of monomial ideals. In this paper, we fully characterize linear quotients in terms of the lcm-lattice of monomial ideals. We also formulate an analogous characterization for monomial ideals with linear resolutions, making explicit a relationship that is implicit in the existing literature. These results complement characterizations of these two properties in terms of the Alexander dual of the corresponding Stanley-Reisner simplicial complex. In addition, we discuss applications to the case of edge ideals. |
| title | Linear quotients, linear resolutions and the lcm-lattice |
| topic | Commutative Algebra Combinatorics |
| url | https://arxiv.org/abs/2507.23520 |