The Gröbner fan of an An-module

Let I be a non-zero left ideal of the Weyl algebra An of order n over a field k and let L:R2n→R be a linear form defined by L(α,β)=∑i=1neiαi+∑i=1nfiβi. If ei+fi≥0, then L defines a filtration F•L on An. Let grL(I) be the graded ideal associated with the filtration induced by F•L on I. Let finally U...

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Autores: Assi, Abdallah, Castro Jiménez, Francisco Jesús, Granger, Michel
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2000
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/48436
Acceso en línea:http://hdl.handle.net/11441/48436
https://doi.org/10.1016/S0022-4049(99)00034-1
Access Level:acceso abierto
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spelling The Gröbner fan of an An-moduleAssi, AbdallahCastro Jiménez, Francisco JesúsGranger, MichelLet I be a non-zero left ideal of the Weyl algebra An of order n over a field k and let L:R2n→R be a linear form defined by L(α,β)=∑i=1neiαi+∑i=1nfiβi. If ei+fi≥0, then L defines a filtration F•L on An. Let grL(I) be the graded ideal associated with the filtration induced by F•L on I. Let finally U denote the set of all linear form L for which ei+fi≥0 for all 1≤i≤n. The aim of this paper is to study, by using the theory of Gröbner bases, the stability of grL(I) when L varies in U. In a previous paper, we obtained finiteness results for some particular linear forms (used in order to study the regularity of a D-module along a smooth hypersurface). Here we generalize these results by adapting the theory of Gröbner fan of Mora-Robbiano to the D-module case. Our main tool is the homogenization technique initiated in our previous paper, and recently clarified in a work by F. Castro-Jiménez and L. Narváez-Macarro.Dirección General de Investigación Científica y TécnicaElsevierÁlgebraFQM333: Álgebra Computacional en Anillos no Conmutativos y AplicacionesDirección General de Investigación Científica y Técnica (DGICYT). España2000info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/48436https://doi.org/10.1016/S0022-4049(99)00034-1reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésJournal of Pure and Applied Algebra, 150 (1), 27-39.DGICYT PB94-1435http://ac.els-cdn.com/S0022404999000341/1-s2.0-S0022404999000341-main.pdf?_tid=298c859a-a745-11e6-ab1c-00000aab0f27&acdnat=1478782797_f4fd04b53a9e14b2a0f7b136fb88bbc2info:eu-repo/semantics/openAccessoai:idus.us.es:11441/484362026-06-17T12:51:07Z
dc.title.none.fl_str_mv The Gröbner fan of an An-module
title The Gröbner fan of an An-module
spellingShingle The Gröbner fan of an An-module
Assi, Abdallah
title_short The Gröbner fan of an An-module
title_full The Gröbner fan of an An-module
title_fullStr The Gröbner fan of an An-module
title_full_unstemmed The Gröbner fan of an An-module
title_sort The Gröbner fan of an An-module
dc.creator.none.fl_str_mv Assi, Abdallah
Castro Jiménez, Francisco Jesús
Granger, Michel
author Assi, Abdallah
author_facet Assi, Abdallah
Castro Jiménez, Francisco Jesús
Granger, Michel
author_role author
author2 Castro Jiménez, Francisco Jesús
Granger, Michel
author2_role author
author
dc.contributor.none.fl_str_mv Álgebra
FQM333: Álgebra Computacional en Anillos no Conmutativos y Aplicaciones
Dirección General de Investigación Científica y Técnica (DGICYT). España
description Let I be a non-zero left ideal of the Weyl algebra An of order n over a field k and let L:R2n→R be a linear form defined by L(α,β)=∑i=1neiαi+∑i=1nfiβi. If ei+fi≥0, then L defines a filtration F•L on An. Let grL(I) be the graded ideal associated with the filtration induced by F•L on I. Let finally U denote the set of all linear form L for which ei+fi≥0 for all 1≤i≤n. The aim of this paper is to study, by using the theory of Gröbner bases, the stability of grL(I) when L varies in U. In a previous paper, we obtained finiteness results for some particular linear forms (used in order to study the regularity of a D-module along a smooth hypersurface). Here we generalize these results by adapting the theory of Gröbner fan of Mora-Robbiano to the D-module case. Our main tool is the homogenization technique initiated in our previous paper, and recently clarified in a work by F. Castro-Jiménez and L. Narváez-Macarro.
publishDate 2000
dc.date.none.fl_str_mv 2000
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/48436
https://doi.org/10.1016/S0022-4049(99)00034-1
url http://hdl.handle.net/11441/48436
https://doi.org/10.1016/S0022-4049(99)00034-1
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of Pure and Applied Algebra, 150 (1), 27-39.
DGICYT PB94-1435
http://ac.els-cdn.com/S0022404999000341/1-s2.0-S0022404999000341-main.pdf?_tid=298c859a-a745-11e6-ab1c-00000aab0f27&acdnat=1478782797_f4fd04b53a9e14b2a0f7b136fb88bbc2
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
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collection idUS. Depósito de Investigación de la Universidad de Sevilla
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