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Abstract
The aim of this article is to study the asymptotic stability of the associated primes of the graded pieces of a non-standard multigraded module. In the most general case, we can assure stability for degrees in every sub-net of a cone in ℕr. As a consequence we prove the stability of the depth of these components in every sub-net of a cone in ℕr.
ACKNOWLEDGMENTS
I would like to thank Prof. J. Elias for his valuable suggestions during the elaboration of this work. I want to thank the referee for a very careful reading of the article and for valuable observations that helped to improve this manuscript.
The first version of this work was done at Departament d’Àlgebra i Geometria of Universitat de Barcelona. It was partially supported by MEC-FEDER projects MTM2007-67493 and MTM2010-20279-C02-01. The author is also supported by a postdoctoral grant from the Ministerio de Educación-FECYT of Spain.
Notes
Communicated by I. Swanson.