1. Cellular resolutions of monomial ideals and their Artinian reductions.
- Author
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Faridi, Sara, Farrokhi D.G., Mohammad D.G., Ghorbani, Roya, and Yazdan Pour, Ali Akbar
- Subjects
- *
BETTI numbers , *MORSE theory , *ALGEBRA - Abstract
The question we address in this paper is: which monomial ideals have minimal cellular resolutions, that is, minimal resolutions obtained from homogenizing the chain maps of CW-complexes? Velasco gave families of examples of monomial ideals that do not have minimal cellular resolutions, but those examples have large minimal generating sets. In this paper, we show that if a monomial ideal has at most four generators, then the ideal and its (monomial) Artinian reductions have minimal cellular resolutions. When the ideal is generated by two monomials, we can give a precise description of the CW-complex supporting minimal free resolution of the ideal and its Artinian reduction. Also, in this case, we compute the multigraded Betti numbers, Cohen-Macaulay type and determine when the corresponding algebra is a level algebra. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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