Ordinary double point
= Ordinary double point
= Node of a plane algebraic curve
{synonym}
For a reduced plane <algebraic curve>, an ordinary double point is a point whose lowest nonzero local homogeneous term has degree $2$ and factors into two distinct linear factors over an <algebraic closure>. The two factors give distinct tangent directions. In characteristic not $2$, $x^2+y^2+\text{higher terms}$ is an example.