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Minimal monomial ideals and linear resolutions

Jeffry Phan
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Abstract

A minimal monomial ideal is the combinatorially simplest monomial ideal whose lcm-lattice equals a given finite atomic lattice $\hat{L}$. The minimal ideal inherits many nice properties of any ideal $I$ whose lcm-lattice also equals $\hat{L}$, e.g. Cohen-Macaulayness and the dual property of having a linear resolution. Conversely, any ideal having a linear resolution is shown to be (essentially) minimal.

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Jeffry Phan. 2005-11-03. Minimal monomial ideals and linear resolutions. https://arxiv.org/abs/math/0511032

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