Local topological algebraicity of analytic function germs (Q2832765)
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scientific article; zbMATH DE number 6652757
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Local topological algebraicity of analytic function germs |
scientific article; zbMATH DE number 6652757 |
Statements
Local topological algebraicity of analytic function germs (English)
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14 November 2016
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analytic germs
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generalized discriminants
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Nash functions
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Artin approximation
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equisingularity
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henselian rings
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Néron desingularization
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Varchenko's theorems
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The aim of the paper is to prove that any real or analytic function germ defined on an analytic space is topologically equivalent to a polynomial germ defined on an affine algebraic variety. A similar assertion for germs of analytic sets has originated in [\textit{T. Mostowski}, Bull. Pol. Acad. Sci., Math. 32, 393--400 (1984; Zbl 0579.32007)]. Above all, the authors also discuss the case of families of germs and show on simple examples that the \(C^1\)-analogs of both statements are false.
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