Polynomial maps with maximal multiplicity and the special closure

Carles Bivià-Ausina; Jorge A.C. Huarcaya

doi:10.1007/s00605-018-1204-9

Polynomial maps with maximal multiplicity and the special closure

Carles Bivià-Ausina, Jorge A.C. Huarcaya

Dynamical systems, differential equations and their applications

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Resumen

In this article we characterize the polynomial maps F: C ⁿ → C ⁿ for which F ^{- 1} (0) is finite and their multiplicity μ(F) is equal to n! V _n (Γ ~ ₊ (F)) , where Γ ~ ₊ (F) is the global Newton polyhedron of F. As an application, we derive a characterization of those polynomial maps whose multiplicity is maximal with respect to a fixed Newton filtration.

Idioma original	Inglés
Páginas (desde-hasta)	413-429
Número de páginas	17
Publicación	Monatshefte fur Mathematik
Volumen	188
N.º	3
DOI	https://doi.org/10.1007/s00605-018-1204-9
Estado	Publicada - 11 mar. 2019

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© 2018, Springer-Verlag GmbH Austria, part of Springer Nature.

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abstract = " In this article we characterize the polynomial maps F: C n → C n for which F - 1 (0) is finite and their multiplicity μ(F) is equal to n! V n (Γ ~ + (F)) , where Γ ~ + (F) is the global Newton polyhedron of F. As an application, we derive a characterization of those polynomial maps whose multiplicity is maximal with respect to a fixed Newton filtration.",

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N2 - In this article we characterize the polynomial maps F: C n → C n for which F - 1 (0) is finite and their multiplicity μ(F) is equal to n! V n (Γ ~ + (F)) , where Γ ~ + (F) is the global Newton polyhedron of F. As an application, we derive a characterization of those polynomial maps whose multiplicity is maximal with respect to a fixed Newton filtration.

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KW - Milnor number

KW - Multiplicity

KW - Newton polyhedron

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Polynomial maps with maximal multiplicity and the special closure

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