Specialization of integral dependence for modules
T. Gaffney, S. Kleiman
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 Af, and Henry, Merle and Sabbah's Condition Wf. 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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