Decomposition of residue currents

2007/10/10 by Mats Andersson, Andersson, Mats, Elizabeth Wulcan +1
Engineering · Mathematics · #32A27 #32C30 #Commutative Algebra (math.AC) #Complex Variables (math.CV) #FOS: Mathematics #Integrated Circuits and Semiconductor Failure Analysis #math.AC #math.CV #msc:32A27 #msc:32C30

paper · pdf · doi:10.48550/arxiv.0710.2016

openalex publication_date 2007/10/10 · arxiv created 2009/07/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a submodule J⊂ \mathcal O₀^{⊕ r} and a free resolution of J one can define a certain vector valued residue current whose annihilator is J. We make a decomposition of the current with respect to Ass(J) that correspond to a primary decomposition of J. As a tool we introduce a class of currents that includes usual residue and principal value currents; in particular these currents admit a certain type of restriction to analytic varieties and more generally to constructible sets.

Related

• Residue currents constructed from resolutions of monomial ideals
• Residue currents with prescribed annihilator ideals
• Residue currents of monomial ideals
• About the characterization of some residue currents
• Courants du type residuel attachés à une intersection complète