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

1 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

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10.1007/s00009-017-0879-9

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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.

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The Special Closure of Polynomial Maps and Global Non-degeneracy

Abstract

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Keywords

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