Residue currents with prescribed annihilator ideals

2005/11/09 by Mats Andersson, Andersson, Mats, Elizabeth Wulcan +1
Computer Science · Mathematics · #32A26 #32A27 #32C35 #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Complex Variables (math.CV) #FOS: Mathematics #Polynomial and algebraic computation #math.CV #msc:32A26 #msc:32A27 #msc:32C35

paper · pdf · doi:10.48550/arxiv.math/0511237

openalex publication_date 2005/11/09 · arxiv created 2007/11/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a coherent ideal sheaf J we construct locally a vector-valued residue current R whose annihilator is precisely the given sheaf. In case J is a complete intersection, R is just the classical Coleff-Herrera product. By means of these currents we can extend various results, previously known for a complete intersection, to general ideal sheaves. Combining with integral formulas we obtain a residue version of the Ehrenpreis-Palamodov fundamental principle.

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