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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Local topological algebraicity of analytic function germs

Authors: Marcin Bilski, Adam Parusiński and Guillaume Rond
Journal: J. Algebraic Geom. 26 (2017), 177-197
Published electronically: June 20, 2016
MathSciNet review: 3570585
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Abstract | References | Additional Information

Abstract: Mostowski showed that every (real or complex) germ of an analytic set is homeomorphic to the germ of an algebraic set. In this paper we show that every (real or complex) analytic function germ, defined on a possibly singular analytic space, is topologically equivalent to a polynomial function germ defined on an affine algebraic variety.

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Additional Information

Marcin Bilski
Affiliation: Department of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland

Adam Parusiński
Affiliation: Université Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06108 Nice, France

Guillaume Rond
Affiliation: Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France
MR Author ID: 759916

Received by editor(s): February 24, 2014
Received by editor(s) in revised form: April 11, 2014, May 20, 2014, and August 15, 2014
Published electronically: June 20, 2016
Additional Notes: The authors were partially supported by ANR project STAAVF (ANR-2011 BS01 009). The first author is partially supported by the NCN grant 2014/13/B/ST1/00543. The third author is partially supported by the ANR project SUSI (ANR-12-JS01-0002-01)
Article copyright: © Copyright 2016 University Press, Inc.