Whitney equisingularity for families of hypersurfaces in toric varieties
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911192417566720 |
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| author | Dalbelo, Thaís Maria Santos, Danilo da Nóbrega |
| author_facet | Dalbelo, Thaís Maria Santos, Danilo da Nóbrega |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04177 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Whitney equisingularity for families of hypersurfaces in toric varieties Dalbelo, Thaís Maria Santos, Danilo da Nóbrega Algebraic Geometry 14B05, 32S05, 13F65, 14M25 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. |
| title | Whitney equisingularity for families of hypersurfaces in toric varieties |
| topic | Algebraic Geometry 14B05, 32S05, 13F65, 14M25 |
| url | https://arxiv.org/abs/2510.04177 |