Computing residue currents of monomial ideals using comparison formulas

Given a free resolution of an ideal aa of holomorphic functions, one can construct a vector-valued residue current R  , which coincides with the classical Coleff–Herrera product if aa is a complete intersection ideal and whose annihilator ideal is precisely aa.We give a complete description of R   in the case when aa is an Artinian monomial ideal and the resolution is the hull resolution (or a more general cellular resolution). The main ingredient in the proof is a comparison formula for residue currents due to the first author.By means of this description, we obtain in the monomial case a current version of a factorization of the fundamental cycle of aa due to Lejeune-Jalabert.