On weighted Bochner-Martinelli residue currents

2009/10/05 by Elizabeth Wulcan, Wulcan, Elizabeth
Mathematics · #32A26 #32A27 #32S45 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Commutative Algebra and Its Applications #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32A26 #msc:32A27 #msc:32S45

paper · pdf · doi:10.48550/arxiv.0910.0888

16 pages, 3 figures

arxiv created 2009/10/05 · openalex publication_date 2009/10/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the weighted Bochner-Martinelli residue current R^p(f) associated with a sequence f=(f₁,...,f_m) of holomorphic germs at the origin in Cⁿ, whose common zero set equals the origin, and p=(p₁,..., p_m)∈ Nⁿ. Our main results are a description of R^p(f) and its annihilator ideal in terms of the Rees valuations of the ideal generated by (f₁^p₁,..., 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.

Related

• On Bochner-Martinelli residue currents and their annihilator ideals
• Residue currents of monomial ideals
• On the Structure of the Bochner-Martinelli Residue Currents
• Residue currents constructed from resolutions of monomial ideals
• Baum-Bott residue currents