Building monomial ideals with fixed betti numbers
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916518000852992 |
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| author | Faridi, Sara Li, Peilin |
| author_facet | Faridi, Sara Li, Peilin |
| contents | Motivated by the fact that as the number of generators of an ideal grows so does the complexity of calculating relations among the generators, this paper identifies collections of monomial ideals with a growing number of generators which have predictable free resolutions. We use elementary collapses from discrete homotopy theory to construct infinitely many monomial ideals, with an arbitrary number of generators, which have similar or the same betti numbers. We show that the Cohen-Macaulay property in each unmixed (pure) component of the ideal is preserved as the ideal is expanded. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07995 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Building monomial ideals with fixed betti numbers Faridi, Sara Li, Peilin Commutative Algebra Algebraic Topology Combinatorics Motivated by the fact that as the number of generators of an ideal grows so does the complexity of calculating relations among the generators, this paper identifies collections of monomial ideals with a growing number of generators which have predictable free resolutions. We use elementary collapses from discrete homotopy theory to construct infinitely many monomial ideals, with an arbitrary number of generators, which have similar or the same betti numbers. We show that the Cohen-Macaulay property in each unmixed (pure) component of the ideal is preserved as the ideal is expanded. |
| title | Building monomial ideals with fixed betti numbers |
| topic | Commutative Algebra Algebraic Topology Combinatorics |
| url | https://arxiv.org/abs/2412.07995 |