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Mathematische Zeitschrift

, Volume 288, Issue 3–4, pp 1361–1375 | Cite as

Higher order approximation of analytic sets by topologically equivalent algebraic sets

  • Marcin Bilski
  • Krzysztof Kurdyka
  • Adam Parusiński
  • Guillaume Rond
Article

Abstract

It is known that every germ of an analytic set is homeomorphic to the germ of an algebraic set. In this paper we show that the homeomorphism can be chosen in such a way that the analytic and algebraic germs are tangent with any prescribed order of tangency. Moreover, the space of arcs contained in the algebraic germ approximates the space of arcs contained in the analytic one, in the sense that they are identical up to a prescribed truncation order.

Keywords

Topological equivalence of singularities Artin approximation Zariski equisingularity 

Mathematics Subject Classification

32S05 32S15 13B40 

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Copyright information

© Springer-Verlag GmbH Deutschland 2017

Authors and Affiliations

  • Marcin Bilski
    • 1
  • Krzysztof Kurdyka
    • 2
  • Adam Parusiński
    • 3
  • Guillaume Rond
    • 4
  1. 1.Department of Mathematics and Computer ScienceJagiellonian UniversityKrakówPoland
  2. 2.Université Savoie Mont Blanc, CNRS, LAMA, UMR 5127Le Bourget-du-LacFrance
  3. 3.Université Nice Sophia Antipolis, CNRS, LJAD, UMR 7351NiceFrance
  4. 4.Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373MarseilleFrance

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