Relative mixed multiplicities and mixed Buchsbaum-Rim multiplicities
Commutative Algebra
2024-01-08 v2 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.2311.15105,
title = {Relative mixed multiplicities and mixed Buchsbaum-Rim multiplicities},
author = {Yairon Cid-Ruiz},
journal= {arXiv preprint arXiv:2311.15105},
year = {2024}
}