Residue currents with prescribed annihilator ideals on singular varieties

Abstract

Given an ideal $\mathcal{J}$ on a complex manifold, Andersson and Wulcan constructed a current $R^\mathcal{J}$ such that the annihilator of $R^\mathcal{J}$ is $\mathcal{J}$, generalizing the duality theorem for Coleff-Herrera products. We describe a way to generalize this construction to ideals on singular varieties.