On the Halphen transform of algebraic space curves

摘要

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 was introduced by Halphen as a branch desingularization method in 5 and has also been studied in 2, 8. We extend this notion to the Halphen transform of a space curve and study several of its properties (birationality, degree, rank, class, desingularization).