Specialization of integral dependence for modules

Details Specialization of integral dependence for modules Specialization of integral dependence for modules

1996-10-03

arxiv.org/abs/alg-geom/9610003v3

Mathematics

Algebraic Geometry

42 pages, PLAIN Tex (with switches for AFour, 2-across). Significant improvements have been made in the statements and proofs

Scientific paper

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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