Nuclei of Normal Rational Curves

A k–nucleus of a normal rational curve in PG(n, F ) is the intersection over all k–dimensional osculating subspaces of the curve (k ∈ {−1, 0, . . . , n− 1}). It is well known that for characteristic zero all nuclei are empty. In case of characteristic p > 0 and #F ≥ n the number of non–zero digits in the representation of n+ 1 in base p equals the number of distinct nuclei. An explicit formula for the dimensions of k–nuclei is given for #F ≥ k + 1.