A dimension formula for the nucleus of a Veronese variety Original Research Article

The nucleus of a Veronese variety is the intersection of all its osculating hyperplanes. Various authors have given necessary and sufficient conditions for the nucleus to be empty. We present an explicit formula for the dimension of this nucleus for arbitrary characteristic of the ground field. As a corollary, we obtain a dimension formula for that subspace in the tth symmetric power of a finite-dimensional vector space V which is spanned by the powers at with aset membership, variantV.