The divisor class groups and the graded canonical modules of multi-section rings

TL;DR

This paper characterizes the divisor class group and graded canonical module of multi-section rings associated with normal projective varieties, utilizing Krull domain theory and Hashimoto's equivariant twisted inverse functor.

Contribution

It provides a description of the divisor class group and graded canonical module for multi-section rings under mild conditions, extending existing algebraic geometry frameworks.

Findings

Explicit description of divisor class group and canonical module

Application of Krull domain theory and Hashimoto's functor

Generalization to multi-section rings on normal projective varieties

Abstract

We shall describe the divisor class group and the graded canonical module of the multi-section ring for a normal projective variety X and Weil divisors D_1,..., D_s on X under a mild condition. In the proof, we use the theory of Krull domain and the equivariant twisted inverse functor due to Hashimoto.