KW Semigroups -- Their Betti Numbers, Apéry Posets and Tangent Cones
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910260722139136 |
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| author | González-Sánchez, Mario Srinivasan, Hema |
| author_facet | González-Sánchez, Mario Srinivasan, Hema |
| contents | Let p<q be coprime integers. Kunz-Waldi semigroups are numerical semigroups containing p and q and contained in <p,q,r>, where 2r=p,q,p+q whichever is even. In this paper, we prove a conjecture on the Betti numbers of the semigroup rings of these semigroups, showing that they coincide with those of the ideal of 2x2 minors of a 2xn generic matrix, where n is the embedding dimension. Moreover, we characterize the Apéry posets of Kunz-Waldi semigroups and determine when their tangent cones are Cohen-Macaulay. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27035 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | KW Semigroups -- Their Betti Numbers, Apéry Posets and Tangent Cones González-Sánchez, Mario Srinivasan, Hema Commutative Algebra 13D02, 13A30, 20M14 Let p<q be coprime integers. Kunz-Waldi semigroups are numerical semigroups containing p and q and contained in <p,q,r>, where 2r=p,q,p+q whichever is even. In this paper, we prove a conjecture on the Betti numbers of the semigroup rings of these semigroups, showing that they coincide with those of the ideal of 2x2 minors of a 2xn generic matrix, where n is the embedding dimension. Moreover, we characterize the Apéry posets of Kunz-Waldi semigroups and determine when their tangent cones are Cohen-Macaulay. |
| title | KW Semigroups -- Their Betti Numbers, Apéry Posets and Tangent Cones |
| topic | Commutative Algebra 13D02, 13A30, 20M14 |
| url | https://arxiv.org/abs/2605.27035 |