  Let $G$ be a semiabelian variety defined over a field of characteristic $0$,
endowed with an endomorphism $\Phi$. We prove there is no proper subvariety
$Y\subset G$ which intersects the orbit of each periodic point of $G$ under the
action of $\Phi$. As an application, we are able to give a topological
characterization of the annihilator ideals of irreducible representations in
certain skew polynomial algebras.
