Veronese varieties over fields with non-zero characteristic: a survey Original Research Article

A subspace in the ambient space of a Veronese variety is said to be invariant if it is fixed (as a set of points) under the group of automorphic collineations of the variety. Among the invariant subspaces are the nuclei of Veronesean; they arise as intersection of all osculating subspaces of a fixed type. Here we give a survey on recent results about nuclei of Veronese varieties and invariant subspaces of normal rational curves. If the characteristic of the ground field is zero, then there are only the trivial invariant subspaces. If the characteristic is a prime p, then there are in general many such subspaces, and there is a close relationship to the array of multinomial coefficients module p.