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Article Dans Une Revue Mathematische Zeitschrift Année : 2018

Higher order approximation of analytic sets by topologically equivalent algebraic sets

Résumé

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.
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Dates et versions

hal-01287899 , version 1 (14-03-2016)

Identifiants

Citer

Marcin Bilski, Krzysztof Kurdyka, Adam Parusinski, Guillaume Rond. Higher order approximation of analytic sets by topologically equivalent algebraic sets. Mathematische Zeitschrift, 2018, 288 (3-4), pp.1361-1375. ⟨10.1007/s00209-017-1937-5⟩. ⟨hal-01287899⟩
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