Let G be any ﬁnite group, G → GL(V) be a representation of G, where V is a ﬁnite-dimensional vector space over an algebraically closed ﬁeld k. Theorem. Assume that either char k=0 or char k=p＞0 with p∤|G|.
Then the quotient variety P(V)/G is projectively normal with respect to the line bundle L, where L is the descent of O(1)⊗m from P(V) with m = |G|!. This partially solves a question raised in the paper of Kannan, Pattanayak and Sardar.
American Mathematical Society 139(6), pp.1989-1992