Blowing-up coefficients of entire series and two theorems of Gabrielov
type: Item
instance of: scholarly article
title: Blowing-up coefficients of entire series and two theorems of Gabrielov
zbMATH Open document ID: 0882.32006
DOI: 10.1007/BF02678197
author: Stanisław Łojasiewicz
author: Jean-Claude Tougeron
author: M. Angeles Zurro
published in: Manuscripta Mathematica
publication date: 1997-05-28T00:00:00Z
full work available at URL: https://eudml.org/doc/156268
review text: In the classical Weierstrass Preparation Theorem (either complex or real) the set of ``good'' directions is dense in the projective space, but it is quite possible not to find a good direction in \(0\times \mathbb{C}^k\) \((0\times \mathbb{R}^k)\). However, sometimes this would be most useful. The authors give a remedy to it, via desingularization (Theorem 2.1 and Corollary 2.4). As an application, short proofs of Gabrielov's theorems [\textit{A. M. Gabrielov}, Funct. Anal. Appl. 2, 282-291 (1968); translation from Funkts. Anal. Prilozh. 2, No. 4, 18-30 (1968; Zbl 0179.08503)], namely the theorems from his pioneer work about subanalytic sets, are given.
reviewed by: Zofia Denkowska
Mathematics Subject Classification ID: 32B20
zbMATH DE Number: 1002957
zbMATH Keywords: subanalytic sets
zbMATH Keywords: blowing-up
zbMATH Keywords: Weierstrass preparation theorem
MaRDI profile type: Publication
cites work: Semianalytic and subanalytic sets
cites work: Arc-analytic functions
cites work: Q3905533
cites work: Q3308335
cites work: Distinguish stratifications as a tool in semi-analytic geometry
cites work: Subanalytic Functions
cites work: On the triangulation of subanalytic morphisms.
OpenAlex ID: W2317823045
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description: scientific article; zbMATH DE number 1002957