Equisingularity, Multiplicity, and Dependence

Details Equisingularity, Multiplicity, and Dependence Equisingularity, Multiplicity, and Dependence

1998-05-13

arxiv.org/abs/math/9805062v1

Mathematics

Algebraic Geometry

15 pages, PLAIN TeX (with switches for AFour, 2-across)

Scientific paper

This is a report on some recent work by Gaffney, Massey, and the author, characterizing the conditions A_f and W_f for a family of ICIS germs equipped with a function. First we introduce the work informally. Then we review the formal definitions of A_f and W_f, and state the theorems that characterize them by the constancy of Milnor numbers. Next we review the definition of the Buchsbaum-Rim multiplicity, and reformulate the theorems by the constancy of certain Buchsbaum-Rim multiplicities. Finally, we review the theory of integral dependence of elements on submodules of free modules, and apply it to prove the reformulated theorems.

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