Computing residue currents of monomial ideals using comparison formulas

Journal article, 2014

Given a free resolution of an ideal a of holomorphic functions, one can construct a vector-valued residue current R, which coincides with the classical Coleff–Herrera product if a is a complete intersection ideal and whose annihilator ideal is precisely a. We give a complete description of R in the case when a 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 a due to Lejeune-Jalabert.