Bounds for syzygies of monomial curves
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916343292362752 |
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| author | Caviglia, Giulio Moscariello, Alessio Sammartano, Alessio |
| author_facet | Caviglia, Giulio Moscariello, Alessio Sammartano, Alessio |
| contents | Let G be a numerical semigroup. In this paper, we prove an upper bound for the Betti numbers of the semigroup ring of G which depends only on the width of G, that is, the difference between the largest and the smallest generator of G. In this way, we make progress towards a conjecture of Herzog and Stamate. Moreover, for 4-generated numerical semigroups, the first significant open case, we prove the Herzog-Stamate bound for all but finitely many values of the width. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_05770 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bounds for syzygies of monomial curves Caviglia, Giulio Moscariello, Alessio Sammartano, Alessio Commutative Algebra Combinatorics 13D02, 13F65, 05E40, 13F55, 20M14 Let G be a numerical semigroup. In this paper, we prove an upper bound for the Betti numbers of the semigroup ring of G which depends only on the width of G, that is, the difference between the largest and the smallest generator of G. In this way, we make progress towards a conjecture of Herzog and Stamate. Moreover, for 4-generated numerical semigroups, the first significant open case, we prove the Herzog-Stamate bound for all but finitely many values of the width. |
| title | Bounds for syzygies of monomial curves |
| topic | Commutative Algebra Combinatorics 13D02, 13F65, 05E40, 13F55, 20M14 |
| url | https://arxiv.org/abs/2307.05770 |