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NormalZ r-graded rings and normal cyclic covers

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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)).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Kanasawa University, Maruno-uchi, 920, Kanasawa, Japan

    Masataka Tomari

  2. Department of Mathematical Sciences, Tokai University, 259-12, Hiratsuka, Japan

    Kei-ichi Watanabe

Authors
  1. Masataka Tomari
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  2. Kei-ichi Watanabe
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Tomari, M., Watanabe, Ki. NormalZ r-graded rings and normal cyclic covers. Manuscripta Math 76, 325–340 (1992). https://doi.org/10.1007/BF02567764

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  • DOI: https://doi.org/10.1007/BF02567764

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