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arXiv · 2510.04177

Whitney equisingularity for families of hypersurfaces in toric varieties

Thaís Maria Dalbelo·Danilo da Nóbrega Santos
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Abstract

In this paper, we establish conditions for a family $\{f_t\}$ of functions, with not necessarily isolated singularities, defined on a toric variety so that the associated family of hypersurfaces $\{f_t^{-1}(0)\}$ 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 $\{F_t\}$ of functions in $\mathbb{C}^n$, with not necessarily isolated singularities, ensuring that the corresponding hypersurface family $\{F_t^{-1}(0)\}$ is Whitney equisingular.

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Thaís Maria Dalbelo, Danilo da Nóbrega Santos. 2025-10-05. Whitney equisingularity for families of hypersurfaces in toric varieties. https://arxiv.org/abs/2510.04177

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