A formula for the associated Buchsbaum-Rim multiplicities of a direct sum of cyclic modules
Futoshi Hayasaka
TL;DR
This paper derives a formula for the last positive Buchsbaum-Rim multiplicity of a direct sum of cyclic modules, linking it to the Hilbert-Samuel multiplicity of an ideal, extending previous results by Kirby and Rees.
Contribution
It generalizes the formula for the last positive Buchsbaum-Rim multiplicity to direct sums of cyclic modules, relating it to Hilbert-Samuel multiplicity.
Findings
Derived a new formula for Buchsbaum-Rim multiplicities
Connected Buchsbaum-Rim multiplicity with Hilbert-Samuel multiplicity
Extended Kirby and Rees's previous results
Abstract
In this article, we compute the Buchsbaum-Rim function of two variables associated to a direct sum of cyclic modules and give a formula for the last positive associated Buchsbaum-Rim multiplicity in terms of the ordinary Hilbert-Samuel multiplicity of an ideal. This is a generalization of a formula for the last positive Buchsbaum-Rim multiplicity given by Kirby and Rees.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory