Equisingularity of sections, $(t^r)$ condition, and the integral closure of modules

Terence Gaffney; David Trotman; Leslie Wilson

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Equisingularity of sections, $(t^r)$ condition, and the integral closure of modules

Terence Gaffney·David Trotman·Leslie Wilson

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Abstract

This paper uses the theory of integral closure of modules to study the sections of both real and complex analytic spaces. The stratification conditions used are the (t^) conditions introduced by Thom and Trotman. Our results include a new simple proof showing how the (t^r) conditions improve under Grassman modification, and a characterization of the (t^r) conditions using the multiplicity of a submodule of the Jacobian module of the singularity. This gives numerical criteria for Verdier Equisingularity of families of sections of the space.

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Terence Gaffney, David Trotman, Leslie Wilson. 2005-08-30. Equisingularity of sections, $(t^r)$ condition, and the integral closure of modules. https://arxiv.org/abs/math/0508615

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