Buchsbaum-Rim Multiplicities as Hilbert-Samuel Multiplicities
C-Y. Jean Chan, Jung-Chen Liu, Bernd Ulrich
Abstract
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.
Create a lesson
Related papers
On the weak Lefschetz property of Artinian Gorenstein algebras of codimension three in arbitrary characteristic
Omkar Javadekar
Linear Independence of Polynomial Compositions and Identifiability of Deep Neural Networks
Kathlén Kohn, Giovanni Luca Marchetti, Alex Massarenti et al.
Comparing v-numbers of symbolic and ordinary powers of squarefree monomial ideals
Trung Chau, Tài Huy Hà, A. V. Jayanthan et al.
Polynomial extensions do not preserve the strong finite type property
Viet-Hoang Tran, Phan Thanh Toan, Thieu N. Vo et al.
Reduction numbers for witnesses to the generalized Loewy length
Richard Bartels, Sarah Dajani, Gabriel Koomson
Multi-graded generic initial ideals, regularity, and the optimal colorful fractional Helly theorem for d-Leray complexes
Daniel McGinnis