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arXiv · 1201.3325

Simplicial complexes with rigid depth

Adnan Aslam·Viviana Ene
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Abstract

We extend a result of Minh and Trung to get criteria for $\depth I=\depth\sqrt{I}$ where $I$ is an unmixed monomial ideal of the polynomial ring $S=K[x_1,..., x_n]$. As an application we characterize all the pure simplicial complexes $Δ$ which have rigid depth, that is, which satisfy the condition that for every unmixed monomial ideal $I\subset S$ with $\sqrt{I}=I_Δ$ one has $\depth(I)=\depth(I_Δ).$

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Adnan Aslam, Viviana Ene. 2012-08-14. Simplicial complexes with rigid depth. https://arxiv.org/abs/1201.3325

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