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arXiv · 2412.13970

On the image of a curve in a normal surface by a plane projection

F. Delgado·H. Maugendre
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Abstract

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.

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F. Delgado, H. Maugendre. 2024-12-18. On the image of a curve in a normal surface by a plane projection. https://arxiv.org/abs/2412.13970

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