On weighted Bochner-Martinelli residue currents

Abstract

We study the weighted Bochner-Martinelli residue current $R^p(f)$ associated with a sequence $f=(f_1,\dots,f_m)$ of holomorphic germs at $0\in{\mathsf C}^n$, whose common zero set equals the origin, and $p=(p_1,\ldots, p_m)\in\mathsf{N}^m$. Our main results are a description of $R^p(f)$ in terms of the Rees valuations of the ideal generated by $(f_1^{p_1},\ldots, f_m^{p_m})$ and an explicit description of $R^p(f)$ when $f$ is monomial. For a monomial sequence $f$ we show that $R^p(f)$ is independent of $p$ if and only if $f$ is a regular sequence.