Specialization of integral dependence for modules

1996/10/03 by Terence Gaffney, Steven L. Kleiman, Gaffney, T. +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.alg-geom/9610003

openalex publication_date 1996/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish the principle of specialization of integral dependence for submodules of finite colength of free modules, as part of the general algebraic-geometric theory of the Buchsbaum--Rim multiplicity. Then we apply the principle to the study of equisingularity of ICIS germs, obtaining results for such equisingularity conditions as Whitney's Condition A, Thom's Condition A_f, and Henry, Merle and Sabbah's Condition W_f. Notably, we describe these conditions for analytic families in terms of various numerical invariants, which, for the most part, depend only on the members of a family, not on its total space.

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• Equisingularity, Multiplicity, and Dependence
• Multidegrees, families, and integral dependence
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