Residue currents constructed from resolutions of monomial ideals

Journal article, 2009

Given 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.