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The Special Closure of Polynomial Maps and Global Non-degeneracy

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Abstract

Let \(F:\mathbb C^n\rightarrow \mathbb C^n\) 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 \((\mathbb C^n,0)\rightarrow \mathbb C\). In particular, we characterize the polynomial maps whose set of special monomials is maximal.

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Acknowledgements

The first author was partially supported by DGICYT Grant MTM2015-64013-P. The second author was partially supported by FAPESP-BEPE 2012/22365-8.

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Authors and Affiliations

  1. Institut Universitari de Matemàtica Pura i Aplicada, Universitat Politècnica de València, Camí de Vera, s/n, 46022, Valencia, Spain

    Carles Bivià-Ausina

  2. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Avda. do Trabalhador São-carlense, 400, São Carlos, SP , 13560-970, Brazil

    Jorge A. C. Huarcaya

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  1. Carles Bivià-Ausina
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  2. Jorge A. C. Huarcaya
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Correspondence to Carles Bivià-Ausina.

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Bivià-Ausina, C., Huarcaya, J.A.C. The Special Closure of Polynomial Maps and Global Non-degeneracy. Mediterr. J. Math. 14, 71 (2017). https://doi.org/10.1007/s00009-017-0879-9

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