The Special Closure of Polynomial Maps and Global Non-degeneracy

Carles Bivià-Ausina; Jorge A.C. Huarcaya

doi:10.1007/s00009-017-0879-9

The Special Closure of Polynomial Maps and Global Non-degeneracy

Carles Bivià-Ausina, Jorge A.C. Huarcaya

Dynamical systems, differential equations and their applications

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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.

Original language	English
Article number	71
Journal	Mediterranean Journal of Mathematics
Volume	14
Issue number	2
DOIs	https://doi.org/10.1007/s00009-017-0879-9
State	Published - 1 Apr 2017

Bibliographical note

Funding 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.

Publisher Copyright:
© 2017, Springer International Publishing.

Keywords

Integral closure
Multiplicity
Newton polyhedron
Polynomial maps

Access to Document

10.1007/s00009-017-0879-9

Cite this

@article{0bde0623bb7643659c8184c9d6734f13,

title = "The Special Closure of Polynomial Maps and Global Non-degeneracy",

abstract = "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.",

keywords = "Integral closure, Multiplicity, Newton polyhedron, Polynomial maps",

author = "Carles Bivi{\`a}-Ausina and Huarcaya, {Jorge A.C.}",

note = "Publisher Copyright: {\textcopyright} 2017, Springer International Publishing.",

year = "2017",

month = apr,

day = "1",

doi = "10.1007/s00009-017-0879-9",

language = "Ingl{\'e}s",

volume = "14",

journal = "Mediterranean Journal of Mathematics",

issn = "1660-5446",

publisher = "Birkhauser Verlag Basel",

number = "2",

}

TY - JOUR

T1 - The Special Closure of Polynomial Maps and Global Non-degeneracy

AU - Bivià-Ausina, Carles

AU - Huarcaya, Jorge A.C.

PY - 2017/4/1

Y1 - 2017/4/1

N2 - 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.

AB - 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.

KW - Integral closure

KW - Multiplicity

KW - Newton polyhedron

KW - Polynomial maps

UR - http://www.scopus.com/inward/record.url?scp=85014692801&partnerID=8YFLogxK

U2 - 10.1007/s00009-017-0879-9

DO - 10.1007/s00009-017-0879-9

M3 - Artículo

AN - SCOPUS:85014692801

SN - 1660-5446

VL - 14

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

IS - 2

M1 - 71

ER -

The Special Closure of Polynomial Maps and Global Non-degeneracy

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this