In this article we characterize the polynomial maps F:Cn→Cn for which F−1(0) is finite and their multiplicity μ(F) is equal to n!Vn(Γ˜+(F)) , where Γ˜+(F) is the global Newton polyhedron of F. As an application, we derive a characterization of those polynomial maps whose multiplicity is maximal with respect to a fixed Newton filtration.

In this article we characterize the polynomial maps F:Cn→Cn for which F−1(0) is finite and their multiplicity μ(F) is equal to n!Vn(Γ˜+(F)) , where Γ˜+(F) is the global Newton polyhedron of F. As an application, we derive a characterization of those polynomial maps whose multiplicity is maximal with respect to a fixed Newton filtration.