Rees algebra and almost linearly presented ideals in three variables
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918071318347776 |
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| author | Kumar, Suraj |
| author_facet | Kumar, Suraj |
| contents | Let $R=\k[x,y,z]$ and $I=(f_0,\dots,f_{n-1})$ be a height two perfect ideal which is almost linearly presented (that is, all but the last column have linear entries, but the last column has entries which are homogeneous of degree $2$). Further we suppose that after modulo an ideal generated by two variables, the presentation matrix has rank one. Also, the ideal $I$ satisfies $\Gs{2}$ but not $\Gs{3}$, then we obtain explicit formulas for the defining ideal of the Rees algebra $\rees(I)$ of $I$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_21491 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rees algebra and almost linearly presented ideals in three variables Kumar, Suraj Commutative Algebra 13A30, 13H10, 13H15, 13C14 Let $R=\k[x,y,z]$ and $I=(f_0,\dots,f_{n-1})$ be a height two perfect ideal which is almost linearly presented (that is, all but the last column have linear entries, but the last column has entries which are homogeneous of degree $2$). Further we suppose that after modulo an ideal generated by two variables, the presentation matrix has rank one. Also, the ideal $I$ satisfies $\Gs{2}$ but not $\Gs{3}$, then we obtain explicit formulas for the defining ideal of the Rees algebra $\rees(I)$ of $I$. |
| title | Rees algebra and almost linearly presented ideals in three variables |
| topic | Commutative Algebra 13A30, 13H10, 13H15, 13C14 |
| url | https://arxiv.org/abs/2506.21491 |