Approximation of analytic sets along Nash subvarieties
type: Item
instance of: scholarly article
title: Approximation of analytic sets along Nash subvarieties
zbMATH Open document ID: 1183.32007
DOI: 10.1016/S0019-3577(09)00016-0
author: Marcin Bilski
published in: Indagationes Mathematicae. New Series
publication date: 2009-12-07T00:00:00Z
review text: The article concerns the approximation of analytic sets \(X\) by algebraic ones \(X_{\nu }\) (precisely by Nash sets) in the sense of convergence of holomorphic chains. The main result is that locally it is possible and, moreover, the convergence preserves the multiplicity of \(X\) and \(X_{\nu }\) at almost all points of a fixed Nash subset \(E\subset X\), i.e., \(\text{mult}_{x}X=\text{mult}_{x}X_{\nu }\) for every \(x\) in a dense open subset of \(E.\)
reviewed by: Tadeusz Krasiński
Mathematics Subject Classification ID: 32B15
Mathematics Subject Classification ID: 14P20
zbMATH DE Number: 5643261
zbMATH Keywords: analytic set
zbMATH Keywords: Nash set
zbMATH Keywords: approximation
zbMATH Keywords: multiplicity of analytic set at point
MaRDI profile type: Publication
cites work: Algebraic approximation of structures over complete local rings
cites work: Q4097533
cites work: On approximation of analytic sets
cites work: Approximation of analytic sets with proper projection by Nash sets
cites work: Approximation of analytic sets by Nash tangents of higher order
cites work: Algebraic approximation of analytic sets and mappings
cites work: Algebraicity versus analyticity
cites work: Q3223124
cites work: Approximation of holomorphic maps by algebraic morphisms
cites work: Higher Order Tangents to Analytic Varieties along Curves
cites work: Q3715247
cites work: Almost analytic local algebraicity of analytic sets and functions
cites work: Q3993490
cites work: Approximation in Compact Nash Manifolds
cites work: Q3134933
cites work: Algebraic approximations of holomorphic maps from Stein domains to projective manifolds
cites work: Q3041467
cites work: Holomorphic flexibility properties of complex manifolds
cites work: Q4507537
cites work: The Runge approximation problem for holomorphic maps into Grassmannians
cites work: Intégration sur un ensemble analytique complexe
cites work: Algebraic approximations in analytic geometry
cites work: Q4001976
cites work: Q3701736
cites work: On saturations of embedded analytic rings
cites work: General Néron desingularization based on the idea of Popescu
cites work: General Néron desingularization
cites work: General Néron desingularization and approximation
cites work: A new proof of D. Popescu’s theorem on smoothing of ring homomorphisms
cites work: On the extension of Nash functions
cites work: On the relative Nash approximation of analytic maps
cites work: Solutions d'un système d'équations analytiques réelles et applications
cites work: Q3204736
cites work: Intersection theory in complex analytic geometry
cites work: Q5682591
cites work: Q5338776
Recommended article: Approximation of analytic sets with proper projection by Nash sets
Recommended article: Approximation of analytic sets by Nash tangents of higher order
Recommended article: On approximation of analytic sets
Recommended article: On the relative Nash approximation of analytic maps
Recommended article: On Nash approximation of complex analytic sets in Runge domains
Recommended article: Approximation of subanalytic sets by normal cones
Recommended article: Approximation of functional compact sets by analytic varieties
Recommended article: Approximation in Compact Nash Manifolds
Recommended article: Algebraic approximation of analytic sets and mappings
Recommended article: On approximating submanifolds by algebraic sets and a solution to the Nash conjecture
description: scientific article; zbMATH DE number 5643261