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arXiv · 2112.12305

Regular Sequences On Squares Of Monomial Ideals

Louiza Fouli·Tài Huy Hà·Susan Morey
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Abstract

We use initially regular sequences that consist of linear sums to explore the depth of $R/I^2$, when $I$ is a monomial ideal in a polynomial ring $R$. We give conditions under which these linear sums form regular or initially regular sequences on $R/I^2$. We then obtain a criterion for when $\depth R/I^2>1$ and a lower bound on $\depth R/I^2$.

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Louiza Fouli, Tài Huy Hà, Susan Morey. 2021-12-23. Regular Sequences On Squares Of Monomial Ideals. https://arxiv.org/abs/2112.12305

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