Abstract
AbstractGiven a polynomial map $$F:\mathbb C^n\longrightarrow \mathbb C^p$$
F
:
C
n
⟶
C
p
with finite zero set, $$p\geqslant n$$
p
⩾
n
, we introduce the notion of global multiplicity $${\text {m}}(F)$$
m
(
F
)
associated to F, which is analogous to the multiplicity of ideals in Noetherian local rings. This notion allows to characterize numerically the Newton non-degeneracy at infinity of F. This fact motivates us to study a combinatorial inequality concerning the normalized volume of global Newton polyhedra and to characterize the corresponding equality using special closures. We also study the Newton non-degeneracy at infinity of gradient maps.
Funder
Ministerio de Ciencia e Innovación
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Geometry and Topology,Algebra and Number Theory,Analysis