Elementary construction of residue currents associated to Cohen-Macaulay ideals

Abstract

For a Cohen-Macaulay ideal of holomorphic functions, we construct by elementary means residue currents whose annihilator is precisely the given ideal. We give two proofs that the currents have the prescribed annihilator, one using the theory of linkage, and another using an explicit division formula involving these residue currents to express the ideal membership.

11 pages. Final version to appear in Annales de Fourier

References in corpus (3)

• A comparison formula for residue currents
• A local Grothendieck duality theorem for Cohen-Macaulay ideals
• Explicit versions of the local duality theorem in ${\mathbb{C}}^n$