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arXiv · 0802.0763

On factoriality of Cox rings

Ivan V. Arzhantsev
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Abstract

Generalized Cox's construction associates with an algebraic variety a remarkable invariant -- its total coordinate ring, or Cox ring. In this note we give a new proof of factoriality of the Cox ring when the divisor class group of the variety is finitely generated and free. The proof is based on a notion of graded factoriality. We show that if the divisor class group has torsion, then the Cox ring is again factorially graded, but factoriality may be lost.

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Ivan V. Arzhantsev. 2008-02-06. On factoriality of Cox rings. https://arxiv.org/abs/0802.0763

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