Abstract:
Hassler Whitney once said: The singularities of a general smooth mapping from a surface into R^3 may be quite wild. But a slight alteration of the map will reduce the singularities to a single type.

The new map is called semiregular and the tame singularity is called a Whitney umbrella.

We call the images of semiregular maps singular surfaces. We explore the interplay between a reduced defining equation F(X,Y,Z)=0 and a parametrization φ : R^2 → R^3 of a singular surface.

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