  We study the residue current R^f of Bochner-Martinelli type associated with a
tuple f=(f_1,...,f_m) of holomorphic germs at the origin in C^n, whose common
zero set equals the origin. Our main results are a geometric description of R^f
in terms of the Rees valuations associated with the ideal (f) generated by f
and a characterization of when the annihilator ideal of R^f equals (f).
