One parameter regularizations of products of residue currents

TL;DR

This paper introduces a method to define Coleff-Herrera type products of residue currents through analytic continuation of functions depending on a single complex variable, simplifying their analysis.

Contribution

It presents a novel approach to constructing residue current products using one-parameter regularizations via analytic continuation.

Findings

Residue current products can be defined by analytic continuation.

The method simplifies the construction of residue currents.

Potential applications in complex analysis and algebraic geometry.

Abstract

We show that Coleff-Herrera type products of residue currents can be defined by analytic continuation of natural functions depending on one complex variable.