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For other geometic uses, see Singular point of a curve.
Repeatedly blowing up the singular points of a curve will eventually resolve the singularities.
A type of singular point of a curve.
In the mathematical theory of singularities a cusp is a type of singular point of a curve.
In classical algebraic geometry, a tacnode (also called a point of osculation or double cusp) is a kind of singular point of a curve.