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arXiv · 2508.07437

Joint reductions and mixed Buchsbaum-Rim multiplicities of modules and a joint-reduction-number-zero theorem

Daniel Katz·Vijay Kodiyalam·J. K. Verma
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Abstract

We offer new definitions of joint reductions and mixed Buchsbaum-Rim multiplicity for certain collections of modules over a Noetherian local ring and illustrate their application to give two different proofs of a joint-reduction-number-zero theorem for integrally closed modules over two-dimensional regular local rings. We also relate the mixed Buchsbaum-Rim multiplicity of modules to the Euler-Poincar\'{e} characteristic of a natural Koszul complex and relate it to the mixed Buchsbaum-Rim multiplicity of ideals by generalising a lemma from intersection theory.

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Daniel Katz, Vijay Kodiyalam, J. K. Verma. 2025-08-10. Joint reductions and mixed Buchsbaum-Rim multiplicities of modules and a joint-reduction-number-zero theorem. https://arxiv.org/abs/2508.07437

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