Projective Closure of Semigroup Algebras
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929350690996224 |
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| author | Saha, Joydip Sengupta, Indranath Srivastava, Pranjal |
| author_facet | Saha, Joydip Sengupta, Indranath Srivastava, Pranjal |
| contents | This paper investigates the projective closure of simplicial affine semigroups in $\mathbb{N}^{d}$, $d \geq 2$. We present a characterization of the Cohen-Macaulay property for the projective closure of these semigroups using Gröbner bases. Additionally, we establish a criterion, based on Gröbner bases, for determining the Buchsbaum property of non-Cohen-Macaulay projective closures of numerical semigroup rings. Lastly, we introduce the concept of $k$-lifting for simplicial affine semigroups in $\mathbb{N}^d$, and investigate its relationship with the original simplicial affine semigroup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11319 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Projective Closure of Semigroup Algebras Saha, Joydip Sengupta, Indranath Srivastava, Pranjal Commutative Algebra This paper investigates the projective closure of simplicial affine semigroups in $\mathbb{N}^{d}$, $d \geq 2$. We present a characterization of the Cohen-Macaulay property for the projective closure of these semigroups using Gröbner bases. Additionally, we establish a criterion, based on Gröbner bases, for determining the Buchsbaum property of non-Cohen-Macaulay projective closures of numerical semigroup rings. Lastly, we introduce the concept of $k$-lifting for simplicial affine semigroups in $\mathbb{N}^d$, and investigate its relationship with the original simplicial affine semigroup. |
| title | Projective Closure of Semigroup Algebras |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2405.11319 |