Monodromy of hyperplane sections of a smooth curve

For a nondegenerate embedded smooth algebraic curve over the complex numbers, the cover that chooses one point of a transverse hyperplane section has transitive monodromy. The analogous incidence space for two distinct ordered points is irreducible, giving two-transitivity. A loop around an ordinary tangent hyperplane exchanges two intersection points. Two-transitivity conjugates this transposition to every transposition, so the monodromy is the full symmetric group. In particular its action on fixed-size subsets is transitive.