  In this note, we prove that for any finite dimensional vector space $V$ over
$\mathbb {C}$, and for a finite cyclic group $G$, the projective variety
$\mathbb P(V)/G$ is projectively normal with respect to the descent of
$\mathcal O(1)^{\otimes |G|}$ by a method using toric variety, and deduce the
EGZ theorem as a consequence.
