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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 theEGZ theorem as a consequence.

Projective normality of finite group quotients and EGZ theorem