EQUISINGULARITY OF SECTIONS, (t(r)) CONDITION, AND THE INTEGRAL CLOSURE OF MODULES

作者：Gaffney Terence^*; Trotman David; Wilson Leslie

来源：Journal of Algebraic Geometry, 2009, 18(4): 651-689.

DOI：10.1090/s1056-3911-08-00488-8

This paper uses the theory of integral closure of modules to study the sections of both real and complex analytic spaces. The stratification conditions, which play a key role, are the (t(r)) conditions introduced by Thom and Trotman. Our results include an algebraic formulation of the (t(r)) in terms of the integral closure of modules, and a new simple proof showing how the (t(r)) conditions improve under Grassmann modification. In the complex analytic case, we characterise (t(r)) in terms of the genericity of the multiplicity of a certain submodule of the Jacobian module, then use the principle of specialisation of integral dependence for modules to give an equimultiplicity criterion for (t(r)). As a consequence we obtain numerical criteria for Verdier equisingularity of families of plane sections in various situations.

• 出版日期2009-10
• 单位东北大学