Pascal's triangle, normal rational curves, and their invariant subspaces (Q1840826)

It is known that if the ground field \(F\) of a projective space \(PG(n,F)\) has characteristic zero, then only trivial subspaces are fixed by the group \(P\Gamma L(\Gamma)\) of automorphic collineations of a normal rational curve \(\Gamma\). This paper investigates the case in which the characteristic is non-zero and \(F\) has at least \(n+2\) elements, and provides constructions of all non-trivial \(P\Gamma L(\Gamma)\)-invariant subspaces, all of which turn out to be included in the nucleus of a normal rational curve, which is the intersection of all osculating hyperplanes. There is wealth of examples of invariant spaces, followed by some theorems regarding their lattice.