Pascal’s Triangle, Normal Rational Curves, and their Invariant Subspaces

Each normal rational curve Γ in PG(n, F) admits a group PΓL(Γ) of automorphic collineations. It is well known that for characteristic zero only the empty and the entire subspace are PΓL(Γ)-invariant. In the case of characteristicp > 0 there may be further invariant subspaces. For#F ≥ n + 2, we give a construction of allPΓL (Γ)-invariant subspaces. It turns out that the corresponding lattice is totally ordered in special cases only.