Products of residue currents of Cauchy-Fantappi\`e-Leray type

TL;DR

This paper introduces a method to define and analyze products of residue currents derived from Cauchy-Fantappiè-Leray formulas, showing that for complete intersections, these products match the residue current of the combined sections.

Contribution

The paper defines products of residue currents of Cauchy-Fantappiè-Leray type and proves their equivalence to residue currents of the direct sum in complete intersection cases.

Findings

Product of residue currents coincides with the residue current of the direct sum in complete intersections

Provides a new framework for combining residue currents from vector bundle sections

Extends the understanding of residue currents in complex geometry

Abstract

With a given holomorphic section of a Hermitian vector bundle, one can associate a residue current by means of Cauchy-Fantappi\`e-Leray type formulas. In this paper we define products of such residue currents. We prove that, in the case of a complete intersection, the product of the residue currents of a tuple of sections coincides with the residue current of the direct sum of the sections.