Analytically principal part of polynomials at infinity (Q2833624)
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scientific article; zbMATH DE number 6654782
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Analytically principal part of polynomials at infinity |
scientific article; zbMATH DE number 6654782 |
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Analytically principal part of polynomials at infinity (English)
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18 November 2016
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real or complex polynomials
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Newton polyhedra
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Newton boundary
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convenient polynomials
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analytical type at infinity
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non-degeneracy at infinity
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smoothly or analytically trivial families at infinity
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The authors prove that real (or complex) polynomial functions which are convenient and non-degenerate at infinity in the sense of \textit{A. G. Kushnirenko} [Invent. Math. 32, 1--31 (1976; Zbl 0328.32007)] are determined up to analytical type by the associated Newton polyhedra at infinity [\textit{T. S. Pham}, J. Math. Soc. Japan 60, No. 4, 1065--1081 (2008; Zbl 1159.32016)]. As a result, a sufficient condition in terms of Newton boundary at infinity of a real or complex polynomial under which its deformation is smoothly (resp. analytically) trivial at infinity is obtained.
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