Cusp

ordinary cusp

A singular point of specific type of an algebraic curve. Namely, a singular point of an algebraic curve over an algebraically closed field is called a cusp if the completion of its local ring is isomorphic to the completion of the local ring of the plane algebraic curve at the origin.

Comments

A cusp can also be defined via the so-called intersection number of two plane curves at a point, cf. [a1], pp. 74-82. A generalization of a cusp is a hypercusp, cf. [a1], p. 82.

References

[a1]	W. Fulton, "Algebraic curves. An introduction to algebraic geometry" , Benjamin (1969) pp. 66