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TitleThe Grobner Fan of an An-Module
Author(s) Abdallah Assi, Francisco Jesus Castro-Jimenez, Michel Granger
TypeArticle in Journal
AbstractLet I be a non-zero left ideal of the Weyl algebra An of order n over a field k and let L:R2n&#8594;R be a linear form defined by L(&#945;,&#946;)=&#8721;i=1nei&#945;i+&#8721;i=1nfi&#946;i. If ei+fi>=0, then L defines a filtration FL on An. Let grL(I) be the graded ideal associated with the filtration induced by FL 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 Image-module along a smooth hypersurface). Here we generalize these results by adapting the theory of Gröbner fan of Mora-Robbiano to the Image-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.
URL dx.doi.org/10.1016/S0022-4049(99)00034-1
JournalJournal of Pure and Applied Algebra
Translation No
Refereed No