Journal of the Mathematical Society of Japan
Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645
Whitney regularity and Thom condition for families of non-isolated mixed singularities
Christophe EyralMutsuo Oka
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2018 Volume 70 Issue 4 Pages 1305-1336

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Abstract

We investigate the equisingularity question for 1-parameter deformation families of mixed polynomial functions 𝑓𝑑(𝔃,𝔃̅) from the Newton polygon point of view. We show that if the members 𝑓𝑑 of the family satisfy a number of elementary conditions, which can be easily described in terms of the Newton polygon, then the corresponding family of mixed hypersurfaces π‘“π‘‘βˆ’1(0) is Whitney equisingular (and hence topologically equisingular) and satisfies the Thom condition.

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© 2018 The Mathematical Society of Japan
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