Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equisingularity, Multiplicity, and Dependence   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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The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph