Nuclei of Normal Rational Curves

Abstract

A $k$-nucleus of a normal rational curve in PG$(n,F)$ is the intersection over all $k$-dimensional osculating subspaces of the curve ($k\in \{-1,0,...,n-1\}$). It is well known that for characteristic zero all nuclei are empty. In case of characteristic $p>0$ and $# F\geq n$ 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 $# F\geq k+1$.