A comparison formula for residue currents

Journal article, 2019

Given two ideals I and J of holomoiphic functions such lhal I ⊆ J. we describe a comparison formula relating thc Andersson-Wulcan currents of I and J. More generally, this comparison formula holds for residue currents associated to two generically exact Hermitian complexes together with a morphism between the complexes. One application of the comparison formula is a generalization of the transformation law for Coleff-Hcrrcra products to Andcrsson-Wulcan currents of Cohcn-Macaulay ideals. We also use it to give an analytic proof by means of residue currents of theorems of Hickel. Vasconcelos and Wiche related to the Jacobian ideal of a holomorphic mapping.