Cusp (algebraic geometry)
= Cusp
{disambiguate=algebraic geometry}
{title2=$y^2=x^3$}
= Cusp
{synonym}
A unibranch <singular point of an algebraic variety> on a plane <algebraic curve>. The ordinary cusp has local equation $y^2=x^3$ and parametrization $(x,y)=(t^2,t^3)$; its branch has a repeated tangent and a vanishing first derivative at the singular point. Higher-order cusps may have different local equations. A <cuspidal cubic> gives the basic projective example.