On nearly Gorenstein affine semigroups
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913580323962880 |
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| author | Jafari, Raheleh Strazzanti, Francesco Armengou, Santiago Zarzuela |
| author_facet | Jafari, Raheleh Strazzanti, Francesco Armengou, Santiago Zarzuela |
| contents | We describe the canonical module of a simplicial affine semigroup ring $\mathbb{K}[S]$ and its trace ideal. As a consequence, we characterize when $\mathbb{K}[S]$ is nearly Gorenstein in terms of arithmetic properties of the semigroup $S$. Then, we find some bounds for the Cohen-Macaulay type of $\mathbb{K}[S]$ when it is nearly Gorenstein. In particular, if it has codimension at most three, we prove that the Cohen-Macaulay type is at most three and this bound is sharp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12081 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On nearly Gorenstein affine semigroups Jafari, Raheleh Strazzanti, Francesco Armengou, Santiago Zarzuela Commutative Algebra We describe the canonical module of a simplicial affine semigroup ring $\mathbb{K}[S]$ and its trace ideal. As a consequence, we characterize when $\mathbb{K}[S]$ is nearly Gorenstein in terms of arithmetic properties of the semigroup $S$. Then, we find some bounds for the Cohen-Macaulay type of $\mathbb{K}[S]$ when it is nearly Gorenstein. In particular, if it has codimension at most three, we prove that the Cohen-Macaulay type is at most three and this bound is sharp. |
| title | On nearly Gorenstein affine semigroups |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2411.12081 |