Acta Mathematica Vietnamica | 2019
A Note on the Singularities of Residue Currents of Integrally Closed Ideals
Abstract
Given a free resolution of an ideal a $\\mathfrak a$ of holomorphic functions, there is an associated residue current R that coincides with the classical Coleff-Herrera product if a $\\mathfrak a$ is a complete intersection ideal and whose annihilator ideal equals a $\\mathfrak a$ . In the case when a $\\mathfrak a$ is an Artinian monomial ideal, we show that the singularities of R are small in a certain sense if and only if a $\\mathfrak a$ is integrally closed.