English

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

Commutative Algebra 2025-08-20 v1

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.

Keywords

Cite

@article{arxiv.2502.06182,
  title  = {Minimal cellular resolutions of monomial ideals with five generators and their Artinian reductions},
  author = {Trung Chau},
  journal= {arXiv preprint arXiv:2502.06182},
  year   = {2025}
}

Comments

are welcome. 11 pages. We refer to arXiv:2502.02122 for a different approach towards the same problem