Residue currents constructed from resolutions of monomial ideals

2007/02/27 by Elizabeth Wulcan, Wulcan, Elizabeth
Computer Science · Mathematics · #13D02 #32A27 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #Complex Variables (math.CV) #FOS: Mathematics #Polynomial and algebraic computation #math.AC #math.CV #msc:13D02 #msc:32A27

paper · pdf · doi:10.48550/arxiv.math/0702847

24 pages, 3 figures

openalex publication_date 2007/02/27 · arxiv created 2008/07/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a free resolution of an ideal J of holomorphic functions, one can construct a vector valued residue current R, whose annihilator is precisely J. In this paper we compute R in case J is a monomial ideal and the resolution is a cellular resolution in the sense of Bayer and Sturmfels. A description of R is given in terms of the underlying polyhedral cell complex and it is related to irreducible decompositions of J.

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• Decomposition of residue currents
• Residue currents with prescribed annihilator ideals
• A note on the singularities of residue currents of integrally closed ideals
• On Bochner-Martinelli residue currents and their annihilator ideals