Let F: Cn→ Cn 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 (Cn, 0) → C. In particular, we characterize the polynomial maps whose set of special monomials is maximal.
Bibliographical noteFunding Information:
The first author was partially supported by DGICYT Grant MTM2015-64013-P. The second author was partially supported by FAPESP-BEPE 2012/22365-8.
© 2017, Springer International Publishing.
- Integral closure
- Newton polyhedron
- Polynomial maps