CPL - Chalmers Publication Library

# On weighted Bochner-Martinelli residue currents

Elizabeth Wulcan (Institutionen för matematiska vetenskaper, matematik)
Mathematica Scandinavica (0025-5521). Vol. 110 (2012), 1, p. 18-34.

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 $0\in\mathbf{C}^n$, whose common zero set equals the origin, and $p=(p_1,\ldots, p_m)\in\mathbb N^n$. 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.

Accession Number: WOS:000303219700002