The membership problem for polynomial ideals in terms of residue currents

2005/03/14 by Andersson, Mats
#14E99 #32A27 #32B99 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0503259

Abstract

We find a relation between the vanishing of a globally defined residue current on ¶ⁿ and solution of the membership problem with control of the polynomial degrees. Several classical results appear as special cases, such as Max Nöther's theorem, and we also obtain a generalization of that theorem. There are also connections to effective versions of the Nullstellensatz. We also provide explicit integral representations of the solutions.

Related

• Sparse effective membership problems via residue currents
• Some variants of Macaulay's and Max Noether's theorems
• On the effective membership problem for polynomial ideals
• Explicit representation of membership in polynomial ideals
• Analytic residue theory in the non-complete intersection case