Plane curves as projections of non singular space curves

Abstract

We generalize and make rigorous a construction by Enriques which allows one to obtain a plane curve as the projection of a non singular curve spanning ℙ4 we show that every non singular curve in ℙr projecting onto a given plane curve can be obtained by the same construction. Finally we prove that every non singular plane curve of degree d is the projection of a (non singular) curve of degree 2d-1 spanning ℙ4, and that no lower degree is possible.