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arXiv · 2502.06182

Minimal cellular resolutions of monomial ideals with five generators and their Artinian reductions

Trung Chau
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Abstract

We prove that monomial ideals with at most five generators and their Artinian reductions have minimal generalized Barile-Macchia resolutions. As a corollary, these ideals have minimal cellular resolutions, extending a result by Faridi, D.G, Ghorbanic, and Pour. This corollary is independently obtained by Montaner, Garc\'{i}a, and Mafi, using a different class of cellular resolutions called pruned resolutions.

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Trung Chau. 2025-02-10. Minimal cellular resolutions of monomial ideals with five generators and their Artinian reductions. https://doi.org/10.1016/j.jpaa.2025.108066

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