On the image of a curve in a normal surface by a plane projection
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917872556572672 |
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| author | Delgado, F. Maugendre, H. |
| author_facet | Delgado, F. Maugendre, H. |
| contents | We consider a finite analytic morphism $φ=(f,g)$ defined from a complex analytic normal surface $(Z,z)$ to ${\mathbb C}^2$. We describe the topology of the image by $φ$ of a reduced curve on $(Z,z)$ by means of iterated pencils defined recursively for each branch of the curve from the initial one $\langle f,g \rangle$. This result generalizes the one obtained in a previous paper for the case in which $(Z,z)$ is smooth and the curve irreducible. As a consequence of the methods we can describe also the topological type of the discriminant curve of $φ$, in particular the topological type of each branch of the discriminant can be obtained from the map without the previous knowledge of the critical locus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13970 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the image of a curve in a normal surface by a plane projection Delgado, F. Maugendre, H. Algebraic Geometry 14H20, 32S05, 32S15, 32S45, 32S55 We consider a finite analytic morphism $φ=(f,g)$ defined from a complex analytic normal surface $(Z,z)$ to ${\mathbb C}^2$. We describe the topology of the image by $φ$ of a reduced curve on $(Z,z)$ by means of iterated pencils defined recursively for each branch of the curve from the initial one $\langle f,g \rangle$. This result generalizes the one obtained in a previous paper for the case in which $(Z,z)$ is smooth and the curve irreducible. As a consequence of the methods we can describe also the topological type of the discriminant curve of $φ$, in particular the topological type of each branch of the discriminant can be obtained from the map without the previous knowledge of the critical locus. |
| title | On the image of a curve in a normal surface by a plane projection |
| topic | Algebraic Geometry 14H20, 32S05, 32S15, 32S45, 32S55 |
| url | https://arxiv.org/abs/2412.13970 |