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A curve which has at least multiplicity 
 at each point where a given curve (having only ordinary singular
points and cusps) has a multiplicity 
 is called the adjoint to the given curve.  When the adjoint curve
is of order 
, it is called a special adjoint curve.
References
Coolidge, J. L.  A Treatise on Algebraic Plane Curves.  New York: Dover, p. 30, 1959.