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

抄録

We investigate the equisingularity question for 1-parameter deformation families of mixed polynomial functions 𝑓_𝑡(𝔃,𝔃̅) 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.