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arXiv · 1007.3327

The canonical module of a Cox ring

Mitsuyasu Hashimoto·Kazuhiko Kurano
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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 $K_X$. 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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Mitsuyasu Hashimoto, Kazuhiko Kurano. 2010-07-20. The canonical module of a Cox ring. https://doi.org/10.1215/21562261-1424884

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