Puiseux Expansions and Nonisolated Points in Algebraic Varieties

We consider the problem of deciding whether a common solution to a multivariate polynomial equation system is isolated or not. We present conditions on a given truncated Puiseux series vector centered at the point ensuring that it is not isolated. In addition, in the case that the set of all common...

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Detalles Bibliográficos
Autores principales: Herrero, María Isabel, Jeronimo, Gabriela Tali, Sabia, Juan Vicente Rafael
Publicado: 2016
Materias:
Algebraic varieties
Curves
Isolated points
Puiseux series
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00927872_v44_n5_p2100_Herrero
http://hdl.handle.net/20.500.12110/paper_00927872_v44_n5_p2100_Herrero
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00927872_v44_n5_p2100_Herrero
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spelling paper:paper_00927872_v44_n5_p2100_Herrero2023-06-08T15:08:21Z Puiseux Expansions and Nonisolated Points in Algebraic Varieties Herrero, María Isabel Jeronimo, Gabriela Tali Sabia, Juan Vicente Rafael Algebraic varieties Curves Isolated points Puiseux series We consider the problem of deciding whether a common solution to a multivariate polynomial equation system is isolated or not. We present conditions on a given truncated Puiseux series vector centered at the point ensuring that it is not isolated. In addition, in the case that the set of all common solutions of the system has dimension 1, we obtain further conditions specifying to what extent the given vector of truncated Puiseux series coincides with the initial part of a parametrization of a curve of solutions passing through the point. © 2016, Copyright © Taylor & Francis Group, LLC. Fil:Herrero, M.I. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Jeronimo, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Sabia, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00927872_v44_n5_p2100_Herrero http://hdl.handle.net/20.500.12110/paper_00927872_v44_n5_p2100_Herrero
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Algebraic varieties
Curves
Isolated points
Puiseux series
spellingShingle Algebraic varieties
Curves
Isolated points
Puiseux series
Herrero, María Isabel
Jeronimo, Gabriela Tali
Sabia, Juan Vicente Rafael
Puiseux Expansions and Nonisolated Points in Algebraic Varieties
topic_facet Algebraic varieties
Curves
Isolated points
Puiseux series
description We consider the problem of deciding whether a common solution to a multivariate polynomial equation system is isolated or not. We present conditions on a given truncated Puiseux series vector centered at the point ensuring that it is not isolated. In addition, in the case that the set of all common solutions of the system has dimension 1, we obtain further conditions specifying to what extent the given vector of truncated Puiseux series coincides with the initial part of a parametrization of a curve of solutions passing through the point. © 2016, Copyright © Taylor & Francis Group, LLC.
author Herrero, María Isabel
Jeronimo, Gabriela Tali
Sabia, Juan Vicente Rafael
author_facet Herrero, María Isabel
Jeronimo, Gabriela Tali
Sabia, Juan Vicente Rafael
author_sort Herrero, María Isabel
title Puiseux Expansions and Nonisolated Points in Algebraic Varieties
title_short Puiseux Expansions and Nonisolated Points in Algebraic Varieties
title_full Puiseux Expansions and Nonisolated Points in Algebraic Varieties
title_fullStr Puiseux Expansions and Nonisolated Points in Algebraic Varieties
title_full_unstemmed Puiseux Expansions and Nonisolated Points in Algebraic Varieties
title_sort puiseux expansions and nonisolated points in algebraic varieties
publishDate 2016
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00927872_v44_n5_p2100_Herrero
http://hdl.handle.net/20.500.12110/paper_00927872_v44_n5_p2100_Herrero
work_keys_str_mv AT herreromariaisabel puiseuxexpansionsandnonisolatedpointsinalgebraicvarieties
AT jeronimogabrielatali puiseuxexpansionsandnonisolatedpointsinalgebraicvarieties
AT sabiajuanvicenterafael puiseuxexpansionsandnonisolatedpointsinalgebraicvarieties
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