On the halphen transform of algebraic space curves

Abstract

The Halphen transform of a plane curve is the curve obtained by intersecting the tangent lines of the curve with the corresponding polar lines with respect to some conic. This transform has been introduced by Halphen as a branch desingularization method and has also been studied by Coolidge and by Josse. We extend this notion to Halphen transform of a space curve and study several of its properties (birationality, degree, rank, class, desingularization).