A Note on the Singularities of Residue Currents of Integrally Closed Ideals

Abstract

Given a free resolution of an ideal a of holomorpic functions there is an associated residue current R that coincides with the classical Coleff-Herrera product if a is a complete intersection ideal and whose annihilator ideal equals a.In the case when a is an Artinian monomial ideal, we show that the singularities of R are small in a certain sense if and only if a is integrally closed.