The membership problem for polynomial ideals in terms of residue currents
Mats Andersson · Annales de l’institut Fourier · 2006
We find a relation between the vanishing of a globally defined residue current on ℙ 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, for which we also obtain a generalization. Furthermore there are some connections to effective versions of the Nullstellensatz. We also provide explicit integral representations of the solutions.