Lipschitz Geometry of Mixed Pham-Brieskorn Singularities
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911641394741248 |
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| author | Rabelo, Inácio |
| author_facet | Rabelo, Inácio |
| contents | We give conditions for topological and bi-Lipschitz equivalences within a class of mixed singularities of Pham-Brieskorn type. As a consequence, we construct infinite families that are topologically trivial but have distinct bi-Lipschitz types. We also investigate this problem in the context of mixed surfaces defined by these singularities in the case of two complex variables, deriving conditions for inner, outer, and ambient bi-Lipschitz equivalences. In particular, we obtain an invariant of the subanalytic outer geometry of the associated mixed surfaces, which is determined by the exponents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08264 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lipschitz Geometry of Mixed Pham-Brieskorn Singularities Rabelo, Inácio Algebraic Geometry 14B05, 14J17, 32B20, 32C05 We give conditions for topological and bi-Lipschitz equivalences within a class of mixed singularities of Pham-Brieskorn type. As a consequence, we construct infinite families that are topologically trivial but have distinct bi-Lipschitz types. We also investigate this problem in the context of mixed surfaces defined by these singularities in the case of two complex variables, deriving conditions for inner, outer, and ambient bi-Lipschitz equivalences. In particular, we obtain an invariant of the subanalytic outer geometry of the associated mixed surfaces, which is determined by the exponents. |
| title | Lipschitz Geometry of Mixed Pham-Brieskorn Singularities |
| topic | Algebraic Geometry 14B05, 14J17, 32B20, 32C05 |
| url | https://arxiv.org/abs/2501.08264 |