On the depth of the tangent cone and the growth of the Hilbert function
For a d-dimensional Cohen-Macaulay local ring (R,m) we study the depth of the associated graded ring of R with respect to an m-primary ideal I in terms of the Vallabrega-Valla conditions and the length of It+1/JIt, where J is a J minimal reduction of I and t≥ 1. As a corollary we generalize Sally�...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 1999 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/7766 |
| Acceso en línea: | https://hdl.handle.net/2445/7766 |
| Access Level: | acceso abierto |
| Palabra clave: | Anells locals Ideals (Àlgebra) Homologia Funcions característiques Geometria algebraica Associated graded rings of ideals Homological methods Hilbert-Samuel and Hilbert-Kunz functions Poincaré series Local rings and semilocal rings |
| Sumario: | For a d-dimensional Cohen-Macaulay local ring (R,m) we study the depth of the associated graded ring of R with respect to an m-primary ideal I in terms of the Vallabrega-Valla conditions and the length of It+1/JIt, where J is a J minimal reduction of I and t≥ 1. As a corollary we generalize Sally's conjecture on the depth of the associated graded ring with respect to a maximal ideal to m-primary ideals. We also study the growth of the Hilbert function. |
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