Some classes of sequences of Linear Type
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909500692234240 |
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| author | Kumar, Neeraj Venugopal, Chitra |
| author_facet | Kumar, Neeraj Venugopal, Chitra |
| contents | Given a graded ring $A$ and a homogeneous ideal $I$, the ideal is said to be of linear type if the Rees algebra of $I$ is isomorphic to the symmetric algebra of $I$. In general, $y$-regularity of Rees algebra of $I$ is $0 \Rightarrow$ $I$ is generated by a $d$-sequence $\Rightarrow I$ is of linear type. We show that $d$-sequence ideals represent a significantly smaller subset of ideals of linear type in terms of $y$-regularity. Moreover, we identify a class of $d$-sequences whose arbitrary powers generate ideals of Gröbner linear type. Notably, while $d$-sequences are inherently weak $d$-sequences, we highlight a specific class of algebras where weak $d$-sequences are indeed $d$-sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_00350 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Some classes of sequences of Linear Type Kumar, Neeraj Venugopal, Chitra Commutative Algebra 13D02, 13-04, 13P20, 13A30, 13A02 Given a graded ring $A$ and a homogeneous ideal $I$, the ideal is said to be of linear type if the Rees algebra of $I$ is isomorphic to the symmetric algebra of $I$. In general, $y$-regularity of Rees algebra of $I$ is $0 \Rightarrow$ $I$ is generated by a $d$-sequence $\Rightarrow I$ is of linear type. We show that $d$-sequence ideals represent a significantly smaller subset of ideals of linear type in terms of $y$-regularity. Moreover, we identify a class of $d$-sequences whose arbitrary powers generate ideals of Gröbner linear type. Notably, while $d$-sequences are inherently weak $d$-sequences, we highlight a specific class of algebras where weak $d$-sequences are indeed $d$-sequences. |
| title | Some classes of sequences of Linear Type |
| topic | Commutative Algebra 13D02, 13-04, 13P20, 13A30, 13A02 |
| url | https://arxiv.org/abs/2303.00350 |