Degenerated algebraic curves
When there is an unique tangent line at a point on a curve, this point is
called regular point. Almost all points on an algebraic curve
Beside regular points, there are points on a curve that can have more than one tangent lines and these points are called singular points.
Example of singular points are double points - points in which the curve
intersects itself. There is an upper bound on the number of double points.
Lower figure shown one non-degenerated curve of order 4 with 3 double points and four possible degenerated curves of order 4.
Created by Sonja Gorjanc, translated by Helena Halas and Iva Kodrnja - 3DGeomTeh - Developing project of the University of Zagreb