Equisingularity, Multiplicity, and Dependence
S L Kleiman
Abstract
This is a report on some recent work by Gaffney, Massey, and the author, characterizing the conditions Af and Wf for a family of ICIS germs equipped with a function. First we introduce the work informally. Then we review the formal definitions of Af and Wf, 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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