On Bochner-Martinelli residue currents and their annihilator ideals

2008/11/05 by Mattias Jonsson, Mattias Jönsson, Jonsson, Mattias +2
Mathematics · #32A26 #32A27 #32S45 #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.0811.0636

22 pages, 1 figure

arxiv created 2008/11/05 · openalex publication_date 2008/11/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the residue current R^f of Bochner-Martinelli type associated with a tuple f=(f₁,...,f_m) of holomorphic germs at the origin in Cⁿ, 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).

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