Classification of Lipschitz unimodal function germs
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866915538955927552 |
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| author | Nguyen, Nhan Ruas, Maria Trivedi, Saurabh |
| author_facet | Nguyen, Nhan Ruas, Maria Trivedi, Saurabh |
| contents | In this paper, we introduce the notion of Lipschitz modality for isolated singularities $ f: (\mathbb{C}^n, 0) \to (\mathbb{C}, 0)$ and provide a complete classification of Lipschitz unimodal singularities of corank~2 with non-zero $4$-jets. As a consequence, such singularities are Lipschitz unimodal if they deform to $J_{10}$ but not to $J_{3,0}$. Furthermore, we show that singularities with vanishing $6$-jets have Lipschitz modality at least~$2$, thus establishing an upper bound for the order of Lipschitz unimodality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06792 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification of Lipschitz unimodal function germs Nguyen, Nhan Ruas, Maria Trivedi, Saurabh Algebraic Geometry 14B05, 32C05 In this paper, we introduce the notion of Lipschitz modality for isolated singularities $ f: (\mathbb{C}^n, 0) \to (\mathbb{C}, 0)$ and provide a complete classification of Lipschitz unimodal singularities of corank~2 with non-zero $4$-jets. As a consequence, such singularities are Lipschitz unimodal if they deform to $J_{10}$ but not to $J_{3,0}$. Furthermore, we show that singularities with vanishing $6$-jets have Lipschitz modality at least~$2$, thus establishing an upper bound for the order of Lipschitz unimodality. |
| title | Classification of Lipschitz unimodal function germs |
| topic | Algebraic Geometry 14B05, 32C05 |
| url | https://arxiv.org/abs/2510.06792 |