Any linear system of point-groups on a curve with only ordinary singularities may be cut by adjoint curves.
Linear Group Theorem
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References
Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, pp. 122 and 251, 1959.Referenced on Wolfram|Alpha
Linear Group TheoremCite this as:
Weisstein, Eric W. "Linear Group Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LinearGroupTheorem.html