Higher order approximation of complex analytic sets by algebraic sets
type: Item
instance of: scholarly article
title: Higher order approximation of complex analytic sets by algebraic sets
zbMATH Open document ID: 1411.32005
author: Marcin Bilski
published in: Bulletin des Sciences Mathématiques
publication date: 2019-01-14T00:00:00Z
review text: The article concerns local approximation of analytic sets by algebraic sets with any prescribed order of tangency. The main theorem is: Let \(X\) be an analytic subset of some open set in \(\mathbb{C}^{m}\) of pure dimension \(n\) such that \(X\) contains \(0\in \mathbb{C}^{m}\). Then there are an open neighborhood \(U\) of \(0\) in \(\mathbb{C}^{m}\) and a sequence \(\{X_{\nu}\}\) of algebraic subsets of \(\mathbb{C}^{m}\) of pure dimension \(n\) such that \( \{X_{\nu}\cap U\}\) converges to \(X\cap U\) in the sense of chains [\textit{P. Tworzewski}, Ann. Pol. Math. 62, No. 2, 177--191 (1995; Zbl 0911.32018)]. Moreover, \(\text{dist} (X\cap (U\cdot r),X_{\nu}\cap (U\cdot r))\leq r^{\nu}\), for every \(r\in (0,1)\), \(\nu \in \mathbb{N}\). Here \(\text{dist}(\cdot ,\cdot)\) denotes the Hausdorff distance of relatively compact subsets of \(\mathbb{C}^{m}\).
reviewed by: Tadeusz Krasiński
Mathematics Subject Classification ID: 32B15
Mathematics Subject Classification ID: 32S05
zbMATH DE Number: 7001141
zbMATH Keywords: analytic set
zbMATH Keywords: approximation
zbMATH Keywords: algebraic set
MaRDI profile type: Publication
full work available at URL: j.bulsci.2014.08.009
OpenAlex ID: W2092694467
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DOI: 10.1016/J.BULSCI.2014.08.009
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description: scientific article; zbMATH DE number 7001141