Higher order approximation of complex analytic sets by algebraic sets

Bilski, Marcin

doi:10.1016/j.bulsci.2014.08.009

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Algebraic Approximation Of Nash Sets1

Introduction1

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Cited by 2 publications

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“…The size of E ′ × E ′′ × F will be independent of m. The idea to obtain algebraic V m (equivalent to or approximating some X) as the image of an algebraic set by a certain polynomial map ρ m appeared before (see e.g. [8], [1], [6]). But here ρ m must be chosen in a special way to ensure that V m is both analytically equivalent and higher order tangent to X.…”

Section: Algebraic Approximation Of Nash Setsmentioning

confidence: 99%

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Higher order approximation of analytic sets by topologically equivalent algebraic sets

et al. 2017

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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.2010 Mathematics Subject Classification. 32S05, 32S15, 13B40.

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Section: Algebraic Approximation Of Nash Setsmentioning

confidence: 99%

“…e.g. [5], [6], [10], [12], [11]. But the classical methods of such approximation do not provide the objects which are homeomorphic.…”

Section: Introductionmentioning

confidence: 99%