2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164177Given a free resolution of an ideal $J$ of holomorphic functions, one can construct a vector valued residue current $R$, whose annihilator is precisely $J$. In this paper we compute $R$ in case $J$ is a monomial ideal and the resolution is a cellular resolution in the sense of Bayer and Sturmfels. A description of $R$ is given in terms of the underlying polyhedral cell complex and it is related to irreducible decompositions of $J$.24 pages, 3 figuresComplex VariablesCommutative Algebra32A27; 13D02text