Degenerated algebraic curvesWhen 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
are regular. 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 nondegenerated 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