Buchsbaumness of finite complement simplicial affine semigroups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908447823364096 |
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| author | Bhardwaj, Om Prakash Cisto, Carmelo |
| author_facet | Bhardwaj, Om Prakash Cisto, Carmelo |
| contents | In this article, we classify all Buchsbaum simplicial affine semigroups whose complement in their (integer) rational polyhedral cone is finite. We show that such a semigroup is Buchsbaum if and only if its set of gaps is equal to its set of pseudo-Frobenius elements. Furthermore, we provide a complete structure of these affine semigroups. In the case of affine semigroups with maximal embedding dimension, we provide an explicit formula for the cardinality of the minimal presentation in terms of the number of extremal rays, the embedding dimension, and the genus. Finally, we observe that, unlike the complete intersection, Cohen-Macaulay, and Gorenstein properties, the Buchsbaum property is not preserved under gluing of affine semigroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09267 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Buchsbaumness of finite complement simplicial affine semigroups Bhardwaj, Om Prakash Cisto, Carmelo Commutative Algebra 13H10, 13D02, 20M25, 05E40 In this article, we classify all Buchsbaum simplicial affine semigroups whose complement in their (integer) rational polyhedral cone is finite. We show that such a semigroup is Buchsbaum if and only if its set of gaps is equal to its set of pseudo-Frobenius elements. Furthermore, we provide a complete structure of these affine semigroups. In the case of affine semigroups with maximal embedding dimension, we provide an explicit formula for the cardinality of the minimal presentation in terms of the number of extremal rays, the embedding dimension, and the genus. Finally, we observe that, unlike the complete intersection, Cohen-Macaulay, and Gorenstein properties, the Buchsbaum property is not preserved under gluing of affine semigroups. |
| title | Buchsbaumness of finite complement simplicial affine semigroups |
| topic | Commutative Algebra 13H10, 13D02, 20M25, 05E40 |
| url | https://arxiv.org/abs/2507.09267 |