Abstract
For a finite morphism $$\varphi =(f,g)$$ from the plane to the plane we describe the topology of the image of a branch in the source by the use of iterated pencils of analytic functions, constructed inductively in a natural way starting from the components of the map. In the case of the study of the topology of the discriminant curve, image by $$\varphi $$ of the critical locus of the map, we show that the special fibres of the pencil $$ \langle f,g\rangle $$ suffice to determine the topological type of each branch of the discriminant curve. This is due to the known relations that exist between the branches of the critical locus of $$\varphi $$ and the special fibres.
Published Version
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