On algebraic representatives of topological types of analytic hypersurface germs (Q2913225)
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scientific article; zbMATH DE number 6086801
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On algebraic representatives of topological types of analytic hypersurface germs |
scientific article; zbMATH DE number 6086801 |
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On algebraic representatives of topological types of analytic hypersurface germs (English)
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26 September 2012
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non-isolated singularities
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algebraisation
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It is shown that any complex analytic hypersurface with 1-dimensional singular locus has the same embedded topological type as the germ of a complex algebraic hypersurface. The idea of proof is to consider the singularity as total space of a 1-parameter deformation of its (isolated) hypersurface section, given as analytic curve in the algebraic versal deformation. By Artin approximation, resolution of singularities and the ideas of Thom's first isotopy lemma the original germ is replaced by one for which the curve is given by algebraic power series.
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