On the image of a curve in a normal surface by a plane projection
| Autor: | Delgado, F., Maugendre, H. |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We consider a finite analytic morphism $\varphi =(f,g)$ defined from a complex analytic normal surface $(Z,z)$ to ${\mathbb C}^2$. We describe the topology of the image by $\varphi$ 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 $\varphi$, 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. Comment: 20 pages, 1 figure |
| Databáze: | arXiv |
| Externí odkaz: |
|