Whitney equisingularity for families of hypersurfaces in toric varieties

In this paper, we establish conditions for a family ₜ\ of functions, with not necessarily isolated singularities, defined on a toric variety so that the associated family of hypersurfaces ₜ⁻¹(0)\ is Whitney equisingular. We work in the setting of toric varieties with arbitrary singular sets. This extends previous results by Eyral and Oka concerning families ₜ\ of functions in Cⁿ, with not necessarily isolated singularities, ensuring that the corresponding hypersurface family ₜ⁻¹(0)\ is Whitney equisingular.