arXiv math/05086152005-08-30math.AGmath.CV

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

Terence Gaffney, David Trotman, Leslie Wilson

备注：: 30 pages

英文摘要：

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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