Divisor class groups and graded canonical modules of multisection rings

Abstract

We describe the divisor class group and the graded canonical module of the multisection ring $T(X;D_1,\dots ,D_s)$ for a normal projective variety $X$ and Weil divisors $D_1,\dots ,D_s$ on $X$ under a mild condition. In the proof, we use the theory of Krull domain and the equivariant twisted inverse functor.