Open Access
Winter 2011 The canonical module of a Cox ring
Mitsuyasu Hashimoto, Kazuhiko Kurano
Kyoto J. Math. 51(4): 855-874 (Winter 2011). DOI: 10.1215/21562261-1424884


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.


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Mitsuyasu Hashimoto. Kazuhiko Kurano. "The canonical module of a Cox ring." Kyoto J. Math. 51 (4) 855 - 874, Winter 2011.


Published: Winter 2011
First available in Project Euclid: 10 November 2011

zbMATH: 1246.14012
MathSciNet: MR2854155
Digital Object Identifier: 10.1215/21562261-1424884

Primary: 14C20
Secondary: 13C20

Rights: Copyright © 2011 Kyoto University

Vol.51 • No. 4 • Winter 2011
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