The canonical module of a Cox ring
Abstract
In this paper, we shall describe the graded canonical module of a Noetherian multi-section 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 shall 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, that avoids the twisted inverse functor.
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