With a given holomorphic section of a Hermitian vector bundle, one can associate a residue current by means of Cauchy–Fantappiè–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.
"Products of residue currents of Cauchy–Fantappiè–Leray type." Ark. Mat. 45 (1) 157 - 178, April 2007. https://doi.org/10.1007/s11512-006-0036-3