The Special Closure of Polynomial Maps and Global Non-degeneracy

Abstract

Let \(F:\mathbb C^n\rightarrow \mathbb C^n\) be a polynomial map such that \(F^{-1}(0)\) is finite. We analyze the connections between the multiplicity of F, the Newton polyhedron of F and the set of special monomials with respect to F, which is a notion motivated by the integral closure of ideals in the ring of analytic function germs \((\mathbb C^n,0)\rightarrow \mathbb C\). In particular, we characterize the polynomial maps whose set of special monomials is maximal.