PROJECTIONS OF SPACE CURVES AND DUALITY

We study the flat geometry of orthogonal projections of a generic space curve to planes. For a single projection, we do this by considering submersions on a (singular) plane curve. This is an alternative method to the classification of divergent diagrams carried out in Dias and Nuño Ballesteros [Plane curve diagrams and geometrical applications, Q. J. Math. 59 (2008), 287–310]. We redraw the bifurcation diagrams of the orthogonal projections of space curves adding the information about their flat geometry. We also study the duals of the projected curves and the way they bifurcate as the direction of projection varies locally in S².