Regularizations of residue currents

TL;DR

This paper demonstrates that under certain conditions, Coleff-Herrera residue currents can be regularized and multiplied consistently, enabling a robust calculus for these currents.

Contribution

It establishes a new regularization and multiplication framework for Coleff-Herrera currents under complete intersection assumptions.

Findings

Regularizations of residue currents can be multiplied to produce regularizations of their products.

The calculus of Coleff-Herrera currents is robust under the specified assumptions.

The results facilitate better manipulation of residue currents in complex analysis.

Abstract

Under assumptions about complete intersection, we prove that Coleff-Herrera type currents satisfy a robust calculus in the sense that natural regularizations of such currents can be multiplied to yield regularizations of the Coleff-Herrera product of the currents.