Étale neighbourhoods and the normal crossings locus()

Given a property of the complete local ring of a variety at a point, how can we show that the set of all points on the variety sharing the same property is open or closed in the Zariski topology? Such questions are ubiquitous especially in resolution of singularities. In the example of the normal cr...

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Detalles Bibliográficos
Autores principales: Bruschek, Clemens, Wagner, Dominique
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Elsevier GmbH 2011
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4587311/
https://www.ncbi.nlm.nih.gov/pubmed/29217873
http://dx.doi.org/10.1016/j.exmath.2010.08.002
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author Bruschek, Clemens
Wagner, Dominique
author_facet Bruschek, Clemens
Wagner, Dominique
author_sort Bruschek, Clemens
collection PubMed
description Given a property of the complete local ring of a variety at a point, how can we show that the set of all points on the variety sharing the same property is open or closed in the Zariski topology? Such questions are ubiquitous especially in resolution of singularities. In the example of the normal crossings property and some variations we give a solution via étale neighbourhoods and Artin approximation.
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spelling pubmed-45873112017-12-05 Étale neighbourhoods and the normal crossings locus() Bruschek, Clemens Wagner, Dominique Expo Math Article Given a property of the complete local ring of a variety at a point, how can we show that the set of all points on the variety sharing the same property is open or closed in the Zariski topology? Such questions are ubiquitous especially in resolution of singularities. In the example of the normal crossings property and some variations we give a solution via étale neighbourhoods and Artin approximation. Elsevier GmbH 2011 /pmc/articles/PMC4587311/ /pubmed/29217873 http://dx.doi.org/10.1016/j.exmath.2010.08.002 Text en © 2011 Elsevier GmbH. http://creativecommons.org/licenses/by-nc-nd/3.0/ This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).
spellingShingle Article
Bruschek, Clemens
Wagner, Dominique
Étale neighbourhoods and the normal crossings locus()
title Étale neighbourhoods and the normal crossings locus()
title_full Étale neighbourhoods and the normal crossings locus()
title_fullStr Étale neighbourhoods and the normal crossings locus()
title_full_unstemmed Étale neighbourhoods and the normal crossings locus()
title_short Étale neighbourhoods and the normal crossings locus()
title_sort étale neighbourhoods and the normal crossings locus()
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4587311/
https://www.ncbi.nlm.nih.gov/pubmed/29217873
http://dx.doi.org/10.1016/j.exmath.2010.08.002
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