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arXiv · 1211.0842

Depth of some square free monomial ideals

Dorin Popescu·Andrei Zarojanu
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Abstract

Let $I\supsetneq J$ be two square free monomial ideals of a polynomial algebra over a field generated in degree $\geq 1$, resp. $\geq 2$ . Almost always when $I$ contains precisely one variable, the other generators having degrees $\geq 2$, if the Stanley depth of $I/J$ is $\leq 2$ then the usual depth of $I/J$ is $\leq 2$ too, that is the Stanley Conjecture holds in these cases.

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Dorin Popescu, Andrei Zarojanu. 2012-11-05. Depth of some square free monomial ideals. https://arxiv.org/abs/1211.0842

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