Cuspidal cubic
= Cuspidal cubic
= Cusp
{synonym}
The affine plane curve $y^2=z^3$ is an irreducible cuspidal cubic. Away from the origin its tangent line is $2y\,dy-3z^2\,dz=0$; at the origin both partial derivatives vanish, so its Zariski tangent space is the whole ambient plane and the origin is singular.