Kyoto Journal of Mathematics

The canonical module of a Cox ring

Mitsuyasu Hashimoto and Kazuhiko Kurano

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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 KX. 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

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

First available in Project Euclid: 10 November 2011

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Zentralblatt MATH identifier

Primary: 14C20: Divisors, linear systems, invertible sheaves
Secondary: 13C20: Class groups [See also 11R29]


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.

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