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Relative mixed multiplicities and mixed Buchsbaum-Rim multiplicities

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arxiv 2311.15105 v2 pith:ICC35CS7 submitted 2023-11-25 math.AC math.AG

Yairon Cid-Ruiz This is my paper · ORCID
classification math.ACmath.AG
keywords mixedmultiplicitiesrelativebuchsbaum-rimbirationalitycalldefinedependence
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We define and study the natural multigraded extension of the relative multiplicities introduced by Simis, Ulrich and Vasconcelos. We call these new invariants relative mixed multiplicities. We show that they have a stable value equal to the mixed Buchsbaum-Rim multiplicity of Kleiman and Thorup. Furthermore, we prove that integral dependence and birationality can be detected via the vanishing of relative mixed multiplicities.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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

    math.AC 2025-08 accept novelty 8.0 of 10

    New definitions of joint reductions and mixed Buchsbaum-Rim multiplicities for modules are used to prove a joint-reduction-number-zero theorem for integrally closed modules over two-dimensional regular local rings.

  2. Mixed Segre zeta functions and their log-concavity

    math.AG 2025-07 accept novelty 7.0 of 10

    A new generating function for mixed Segre classes is proved rational, invariant under integral closure, and its associated numerator gives denormalized Lorentzian polynomials.

  3. Degree functions of graded families of ideals

    math.AC 2025-06 conditional novelty 6.0 of 10

    Multiplicities and degree functions of graded families of ideals are expressed as limits of intersection products, with a closed formula for Q-divisorial filtrations in dimension 2.

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