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This research aims to characterize the topology of the image of a reduced curve under a finite analytic morphism from a normal surface to C².

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

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This research aims to characterize the topology of the image of a reduced curve under a finite analytic morphism from a normal surface to C².
Defined a finite analytic morphism from a complex analytic normal surface to C².
Described topology using iterated pencils recursively for each branch of the curve.
Analyzed the topological type of the discriminant curve of the morphism.
Expanded previous findings for smooth cases to include reduced curves.
Outlined how the topological type of each discriminant branch can be derived from the morphism map.
Provided a new generalization for understanding curve images in complex surfaces.

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This analysis describes the topology of curve images in complex surfaces, suggesting new methods for understanding projections.

Mata et al. (2026) studied this question.

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