1999/05/10 by Carlos A. Berenstein, C. A. Berenstein, Berenstein, C. A. +3
Computer Science · Mathematics · #14BO5 #32A27(Secondary) #32C30 (Primary) 14Q20 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Polynomial and algebraic computation #math.AG #math.CV #msc:14BO5 #msc:14Q20 #msc:32C30
paper · pdf · doi:10.48550/arxiv.math/9905051
32 pages
arxiv created 1999/05/10 · openalex publication_date 1999/05/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In previous work of the authors and their collaborators (see Progress in Math, vol. 114, Birkäuser, 1993) it was shown how the equivalence of several constructions of residue currents associated to complete intersection families of (germs of) holomorphic functions in \bf Cn could be profitably used to solve algebraic problems like effective versions of the Nullstellensatz. In this work we explain how an application of similar ideas in the non-complete intersection case leads to a remarkable algebraic result, namely: Let P1,...,Pn be n polynomials in n variables such that the zero set of P1,...,Pn can be defined as the zero set of P1,...,Pν, with ν< n. Then, the Jacobian J(P1,...,Pn) of (P1,...,Pn) is in the ideal generated by the Pj, j=1,...,n. The same methods lead to further insights into the construction of Green currents associated to effective cycles in projective space.