Divisor class groups and graded canonical modules of multisection rings (Q2873894)

The author considers a normal projective variety \(X\) and the graded multisection ring \(T(X; D_{1}, \ldots, D_{s})\) with \(D_{1}, \ldots, D_{s}\) the Weil divisors such that \(\mathbb{N}D_{1}+ \ldots+ \mathbb{N}D_{s}\) contains an ample Cartier Divisor. In the main theorem he gives a complete description of the divisor class group and of the graded canonical module of \(T(X; D_{1}, \ldots, D_{s})\), that is proved to be a Krull domain. Interesting examples of varieties \(X\) are given involving the Cox ring \(\mathrm{Cox}(X)\) to study the graded canonical module of \(T(X; D_{1}, \ldots, D_{s})\).