Superisolated singularities and friends
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915211375542272 |
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| author | Bartolo, Enrique Artal |
| author_facet | Bartolo, Enrique Artal |
| contents | Superisolated surface singularities in $(\mathbb{C}^3,0)$ were introduced by I. Luengo to prove that the $μ$-constant stratum may be singular. The main feature of this family is that it can bring information from the projective plane curves (global setting but smaller dimension) into surface singularities. They are simple enough to allow to retreive information and complicated enough to offer a variety of properties. The so-called Lê-Yomdin singularities are a generalization which offers a wider catalog of examples. We study some properties of these singularities, mainly topological and related with the monodromy, and we introduce another family which exploits the same properties but in the quasi-homogeneous setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18176 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Superisolated singularities and friends Bartolo, Enrique Artal Algebraic Geometry 14J17, 32S25, 32S50 Superisolated surface singularities in $(\mathbb{C}^3,0)$ were introduced by I. Luengo to prove that the $μ$-constant stratum may be singular. The main feature of this family is that it can bring information from the projective plane curves (global setting but smaller dimension) into surface singularities. They are simple enough to allow to retreive information and complicated enough to offer a variety of properties. The so-called Lê-Yomdin singularities are a generalization which offers a wider catalog of examples. We study some properties of these singularities, mainly topological and related with the monodromy, and we introduce another family which exploits the same properties but in the quasi-homogeneous setting. |
| title | Superisolated singularities and friends |
| topic | Algebraic Geometry 14J17, 32S25, 32S50 |
| url | https://arxiv.org/abs/2503.18176 |