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arXiv · 2303.00350

Some classes of sequences of Linear Type

Neeraj Kumar·Chitra Venugopal
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Abstract

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 Gr\"obner 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.

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Neeraj Kumar, Chitra Venugopal. 2023-03-01. Some classes of sequences of Linear Type. https://arxiv.org/abs/2303.00350

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