# Cusp

ordinary cusp

A singular point of specific type of an algebraic curve. Namely, a singular point $x$ of an algebraic curve $X$ over an algebraically closed field $k$ is called a cusp if the completion of its local ring $\mathcal O_{X,x}$ is isomorphic to the completion of the local ring of the plane algebraic curve $y^2+x^3=0$ at the origin.