## Kyoto Journal of Mathematics

### The canonical module of a Cox ring

#### Abstract

In this paper, we describe the graded canonical module of a Noetherian multisection ring of a normal projective variety. In particular, in the case of the Cox ring, we prove that the graded canonical module is a graded free module of rank one with the shift of degree $K_{X}$. We give two kinds of proofs. The first one utilizes the equivariant twisted inverse functor developed by the first author. The second proof is down-to-earth, which avoids the twisted inverse functor, but some additional assumptions are required in this proof.

#### Article information

Source
Kyoto J. Math., Volume 51, Number 4 (2011), 855-874.

Dates
First available in Project Euclid: 10 November 2011

https://projecteuclid.org/euclid.kjm/1320936735

Digital Object Identifier
doi:10.1215/21562261-1424884

Mathematical Reviews number (MathSciNet)
MR2854155

Zentralblatt MATH identifier
1246.14012

Subjects
Primary: 14C20: Divisors, linear systems, invertible sheaves

#### Citation

Hashimoto, Mitsuyasu; Kurano, Kazuhiko. The canonical module of a Cox ring. Kyoto J. Math. 51 (2011), no. 4, 855--874. doi:10.1215/21562261-1424884. https://projecteuclid.org/euclid.kjm/1320936735

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