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arXiv · 1607.03741

Whitney regularity and Thom condition for families of non-isolated mixed singularities

Christophe Eyral·Mutsuo Oka
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Abstract

We investigate the equisingularity question for $1$-parameter deformation families of mixed polynomial functions $f_t(\mathbf{z},\bar{\mathbf{z}})$ from the Newton polygon point of view. We show that if the members $f_t$ 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 $f_t^{-1}(0)$ is Whitney equisingular (and hence topologically equisingular) and satisfies the Thom condition.

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Christophe Eyral, Mutsuo Oka. 2016-07-13. Whitney regularity and Thom condition for families of non-isolated mixed singularities. https://arxiv.org/abs/1607.03741

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