NormalZ r-graded rings and normal cyclic covers

Abstract

We give a description of a cyclic cover of a normal domain in terms of a rational coefficient divisor and an element of the quotient field of the base domain. Then we study the integrity, the normality, the divisor class group and the Gorenstein property of the cyclic cover by our description ((1.9), (1.12), (2.6), (3.2), (3.3)). Also we characterize the regularity, of it in terms of the divisor and singularities of base domain ((3.11)). As an application, we can give the necessary and sufficient condition for a normal graded ring over a field to have an isolated singularity in terms of Demazure's construction of normal graded rings ((4.1)).