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High Quality Content by WIKIPEDIA articles! In mathematics, a singular point of an algebraic variety V is a point P that is 'special' (so, singular), in the geometric sense that V is not locally flat there. In the case of an algebraic curve, a plane curve that has a double point, such as the cubic curve y2 = x2(x + 1) exhibits at (0, 0), cannot simply be parametrized near the origin. A plot of this curve is below with the singular point at the origin. Points of V that are not singular are called non-singular or regular. It is always true that most points are non-singular in the sense that the non-singular points form a set that is both open and non-empty.