On weighted Bochner-Martinelli residue currents

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We study the weighted Bochner-Martinelli residue current Rᵖ(f) associated with a sequence f=(f₁,...,fₘ) of holomorphic germs at the origin in Cⁿ, whose common zero set equals the origin, and p=(p₁,..., pₘ)∈ Nⁿ. Our main results are a description of Rᵖ(f) and its annihilator ideal in terms of the Rees valuations of the ideal generated by (f₁ᵖ¹,..., fₘᵖᵐ) and an explicit description of Rᵖ(f) when f is monomial. For a monomial sequence f we show that Rᵖ(f) is independent of p if and only if f is a regular sequence.