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Borys Kadets works on algebraic geometry and arithmetic questions involving Galois groups. His paper on monodromy of hyperplane sections of a smooth curve studies permutations of the intersection points between a projective curve and a moving hyperplane.^[ref]

For an appropriate irreducible projective curve in characteristic zero, the monodromy is the full symmetric group. In positive characteristic it can be smaller, and the paper analyzes these alternatives. This makes the characteristic of the coefficient field visible in how geometric intersection points can be permuted.^[ref]

Let $C\subset {\mathbb{P}}_{\mathbb{C}}^r$, $r\ge 2$, be a smooth irreducible nondegenerate projective variety of dimension one and degree $d\ge 2$. Let $U$ be the open subset of the dual projective space consisting of hyperplanes meeting $C$ in $d$ distinct points. The incidence projectionis a $d$-sheeted covering space in the complex analytic topology. Its monodromy is the full symmetric group $S_d$.^[ref]

The incidence space choosing two distinct ordered intersection points is irreducible, so the monodromy action of a covering space is two-transitive. A small loop around an ordinary tangent hyperplane exchanges its two nearby intersection points and fixes the others. Conjugating this transposition by double transitivity gives every transposition, and these generate $S_d$. In particular the action on $k$-element subsets is transitive for each $0\le k\le d$. For a degree-one projective line, a transverse section has one point and the corresponding group is the trivial $S_1$.