The membership problem for polynomial ideals in terms of residue currents

Details The membership problem for polynomial ideals in terms of residue currents The membership problem for polynomial ideals in terms of residue currents

2005-03-14

arxiv.org/abs/math/0503259v1

Mathematics

Complex Variables

Scientific paper

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 N\"other'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.

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