Abstract
We give a description of a graded cyclic cover of a normal graded ring in terms of the Pinkham-Demazure description of normal graded rings R=R(X, D). With the geometric description of Cl(R), it is shown that our cyclic cover S possesses the Pinkham-Demazure description S≅R(Y, ˜{D}) [Theorem 1.3], by which we obtain a description of an index one cover [Corollary 1.7] of R. In §2, as an application of this description, we give criteria for the normal graded singularities to be Kawamata log terminal or to be log canonical. Further, in §3 we study the relations between cyclic covers of the Kummer type and cyclic covers obtained by using Veronese subrings. Our results extend S. Mori's structure theorem regarding graded factorial domains.
