The Special Closure of Polynomial Maps and Global Non-degeneracy

被引:0
作者
Carles Bivià-Ausina
Jorge A. C. Huarcaya
机构
[1] Universitat Politècnica de València,Institut Universitari de Matemàtica Pura i Aplicada
[2] Universidade de São Paulo,Instituto de Ciências Matemáticas e de Computação
来源
Mediterranean Journal of Mathematics | 2017年 / 14卷
关键词
Polynomial maps; Multiplicity; Integral closure; Newton polyhedron; Primary 32S99; Secondary 47H11; 14B05;
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摘要
Let F:Cn→Cn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F:\mathbb C^n\rightarrow \mathbb C^n$$\end{document} be a polynomial map such that F-1(0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F^{-1}(0)$$\end{document} 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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\mathbb C^n,0)\rightarrow \mathbb C$$\end{document}. In particular, we characterize the polynomial maps whose set of special monomials is maximal.
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