On the use of naturality in algorithmic resolution
type: Item
instance of: scholarly article
title: On the use of naturality in algorithmic resolution
zbMATH Open document ID: 1205.14017
author: Augusto Nobile
published in: Journal of Algebra
publication date: 2011-01-07T00:00:00Z
review text: the author shows in a very synthetic manner some results concerning algorithmic resolution in characteristic zero (in the sense of \textit{S. Encinas} and \textit{O. Villamayor} [Prog. Math. 181, 147--227 (2000; Zbl 0969.14007)], and \textit{A. Bravo, S. Encinas} and \textit{O. Villamayor} [Rev. Mat. Iberoam. 21, No. 2, 349--458 (2005; Zbl 1086.14012)]) and their relationship with the weak equivalence introduced by Hironaka in the latest 70's, see for example [\textit{H. Hironaka}, ``Idealistic exponents of singularity'', Algebraic geometry, The Johns Hopkins centen. Lect., Symp. Baltimore/Maryland 1976, 52--125 (1977; Zbl 0496.14011)]. It simplifies some arguments and gives a very simple way to prove the ``naturality'' of the main step of the proof: the inductive step.
reviewed by: Angélica Benito
Mathematics Subject Classification ID: 14E15
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 14B99
Mathematics Subject Classification ID: 14E99
zbMATH DE Number: 5833451
zbMATH Keywords: singularities
zbMATH Keywords: marked ideals
zbMATH Keywords: blowing-up
zbMATH Keywords: permissible centers
zbMATH Keywords: resolution
zbMATH Keywords: equivalence
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2010.06.008
OpenAlex ID: W2028306450
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DOI: 10.1016/J.JALGEBRA.2010.06.008
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description: scientific article; zbMATH DE number 5833451