Projective closure of Gorenstein monomial curves and the Cohen-Macaulay property
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913409893662720 |
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| author | Katsabekis, Anargyros |
| author_facet | Katsabekis, Anargyros |
| contents | Let $C({\bf a})$ be a Gorenstein non-complete intersection monomial curve in the 4-dimensional affine space. There is a vector ${\bf v} \in \mathbb{N}^{4}$ such that for every integer $m \geq 0$, the monomial curve $C({\bf a}+m{\bf v})$ is Gorenstein non-complete intersection whenever the entries of ${\bf a}+m{\bf v}$ are relatively prime. In this paper, we study the arithmetically Cohen-Macaulay property of the projective closure of $C({\bf a}+m{\bf v})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00528 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Projective closure of Gorenstein monomial curves and the Cohen-Macaulay property Katsabekis, Anargyros Algebraic Geometry Let $C({\bf a})$ be a Gorenstein non-complete intersection monomial curve in the 4-dimensional affine space. There is a vector ${\bf v} \in \mathbb{N}^{4}$ such that for every integer $m \geq 0$, the monomial curve $C({\bf a}+m{\bf v})$ is Gorenstein non-complete intersection whenever the entries of ${\bf a}+m{\bf v}$ are relatively prime. In this paper, we study the arithmetically Cohen-Macaulay property of the projective closure of $C({\bf a}+m{\bf v})$. |
| title | Projective closure of Gorenstein monomial curves and the Cohen-Macaulay property |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2407.00528 |