There is a one-to-one correspondence between the sets of equivalent correspondences (not of value 0) on an irreducible
curve of curve genus 
, 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.
Rosatti's Theorem
Explore with Wolfram|Alpha
References
Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, p. 339, 1959.Referenced on Wolfram|Alpha
Rosatti's TheoremCite this as:
Weisstein, Eric W. "Rosatti's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RosattisTheorem.html