Images of maps from $(\mathbb{C}^2,0)$ to $(\mathbb{C}^n,0)$
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915585630142464 |
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| author | Pedersen, Helge Møller |
| author_facet | Pedersen, Helge Møller |
| contents | Let $F:(\mathbb{C}^2,0)\to (\mathbb{C}^n,0)$ be the germ of a finite map and $(X,0)$ be its image. We will in this article using the topology of the link show that $(X,0)$ has to be a quotient singularity if it is normal and describe the possible topological types. Including a discussion of the groups and examples of how to construct a map to a given topology. We will also discuss the case when the image is not normal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14941 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Images of maps from $(\mathbb{C}^2,0)$ to $(\mathbb{C}^n,0)$ Pedersen, Helge Møller Algebraic Geometry Geometric Topology 14B05 (Primary) 32S05, 32S25, 32S50, 57K30, 57M10, 57M60 (Secondary) Let $F:(\mathbb{C}^2,0)\to (\mathbb{C}^n,0)$ be the germ of a finite map and $(X,0)$ be its image. We will in this article using the topology of the link show that $(X,0)$ has to be a quotient singularity if it is normal and describe the possible topological types. Including a discussion of the groups and examples of how to construct a map to a given topology. We will also discuss the case when the image is not normal. |
| title | Images of maps from $(\mathbb{C}^2,0)$ to $(\mathbb{C}^n,0)$ |
| topic | Algebraic Geometry Geometric Topology 14B05 (Primary) 32S05, 32S25, 32S50, 57K30, 57M10, 57M60 (Secondary) |
| url | https://arxiv.org/abs/2401.14941 |