Higher order approximation of analytic sets by topologically equivalent algebraic sets
Complex Variables
2017-05-19 v2
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.
Cite
@article{arxiv.1602.06933,
title = {Higher order approximation of analytic sets by topologically equivalent algebraic sets},
author = {Marcin Bilski and Krzysztof Kurdyka and Adam Parusinski and Guillaume Rond},
journal= {arXiv preprint arXiv:1602.06933},
year = {2017}
}
Comments
15 pages, to appear in Math. Z