2022/09/21 by Sara Faridi, Faridi, Sara, Mohammad Farrokhi Derakhshandeh Ghouchan +5
Computer Science · Mathematics · #05E45 #13D02 #13F55 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary 13C70 #Secondary 05E40 #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2209.10338
openalex publication_date 2022/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.