Buchsbaum-Rim Multiplicities as Hilbert-Samuel Multiplicities

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

Over a regular local ring of dimension two with maximal ideal m, we study the Buchsbaum-Rim multiplicity of a finitely generated module M of finite colength in a free module F. First, we investigate the colength of an m-primary ideal and its Hilbert-Samuel multiplicity using linkage theory. As applications, we establish several multiplicity formula that express the Buchsbaum-Rim multiplicity of M in terms of the Hilbert-Samuel multiplicities of ideals related to a certain minimal reduction U of M. Moreover, there exists m-primary Bourbaki ideals I and J of the modules F and M respectively such that F/M is isomorphic to I/J. We also have a formula for the Buchsbaum-Rim multiplicity whenever such I and J are given. The latter part is related to a graphical interpretation of the multiplicities in the case of monomial ideals.
submitted for publication

Keywords

Commutative Algebra, 13C40, 13H15

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/113919

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0606413
 http://arxiv.org/abs/math/0606413

Collections

arXiv