Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nilpotents, Integral Closure and Equisingularity conditions   In earlier work, the author described various stratification conditions for a
complex analytic set X in terms of the theory of integral closure of modules.
However, even if an analytic set has a reduced structure, often geometric
operations like intersection give a non-reduced structure on the resulting
analytic space. In this note we show that it is not necessary for X to have a
reduced structure to apply the earlier integral closure results. As an
application we give a simple proof of a necessary and sufficient condition for
the Whitney conditions to pass to the intersection of X with a hyperplane
containing the smooth stratum Y, and for this intersection to be "typical". In
the case where X is a family of ICIS singularities, we show the condition on H
at a point y of Y depends only on the fiber of the family over y.

37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess