A comparison formula for residue currents

Abstract

Given two ideals $\mathcal{I}$ and $\mathcal{J}$ of holomorphic functions such that $\mathcal{I}\subseteq \mathcal{J}$, we describe a comparison formula relating the Andersson-Wulcan currents of $\mathcal{I}$ and $\mathcal{J}$. 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-Herrera products to Andersson-Wulcan currents of Cohen-Macaulay ideals. We also use it to give an analytic proof by means of residue currents of theorems of Hickel, Vasconcelos and Wiebe related to the Jacobian ideal of a holomorphic mapping.

22 pages, v6: Minor sign correction in equation (3.4)

References in corpus (1)

• A local duality principle for ideals of pure dimension

Cited by in corpus (4)

• Residue currents and fundamental cycles
• Explicit versions of the local duality theorem in ${\mathbb{C}}^n$
• An explicit isomorphism of different representations of the Ext functor using residue currents
• Elementary construction of residue currents associated to Cohen-Macaulay ideals