On the Structure of the Bochner-Martinelli Residue Currents

TL;DR

This paper investigates the structure of Bochner-Martinelli residue currents, revealing their representations as sums involving residue currents, principal value currents, and hypergeometric functions, through Mellin transform techniques.

Contribution

It provides a detailed structure formula for residue currents related to monomial mappings, expanding understanding of their composition and representations.

Findings

Residue currents can be expressed as sums of specific component currents.

The structure involves hypergeometric functions and principal value currents.

Mellin transforms are key tools in analyzing these residue currents.

Abstract

We study residue currents of the Bochner--Martinelli type using their relationship with Mellin transforms of residue integrals. We present the structure formula for residue currents associated with monomial mappings: they admit representations as sums of products of residue currents, principal value currents and hypergeometric functions.