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There is a one-to-one correspondence between the sets of equivalent correspondences (not of value 0) on an irreducible
curve of Genus (Curve) 
, and the rational Collineations of a projective space of 
dimensions which
leave invariant a space of 
dimensions. The number of linearly independent correspondences will be that of linearly
independent Collineations.
References
Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, p. 339, 1959.