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...
| Autores: | , , |
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| 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 |
| Sumario: | 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. |
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