  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 $t$-th symmetric power
of a finite-dimensional vector space $V$ which is spanned by the powers $a^t$
with $\a\in\V$.
