Uniqueness and factorization of Coleff-Herrera currents

Details Uniqueness and factorization of Coleff-Herrera currents Uniqueness and factorization of Coleff-Herrera currents

2007-11-15

arxiv.org/abs/0711.2440v1

Mathematics

Complex Variables

Scientific paper

We prove a uniqueness result for Coleff-Herrera currents which in particular means that if $f=(f_1,..., f_m)$ defines a complete intersection, then the classical Coleff-Herrera product associated to $f$ is the unique Coleff-Herrera current that is cohomologous to 1 with respect to the operator $\delta_f-\dbar$, where $\delta_f$ is interior multiplication with $f$. From the uniqueness result we deduce that any Coleff-Herrera current on a variety $Z$ is a finite sum of products of residue currents with support on $Z$ and holomorphic forms.

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