= 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.
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