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Matematicheskie Zametki, 2009, Volume 85, Issue 5, Pages 643–651
DOI: https://doi.org/10.4213/mzm6907 (Mi mzm6907) 		 
This article is cited in 11 scientific papers (total in 11 papers)

On the Factoriality of Cox rings

I. V. Arzhantsev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (474 kB) Citations (11)
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DOI: https://doi.org/10.4213/mzm6907
Abstract: The generalized Cox 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 the factoriality of the Cox ring when the divisor class group of the variety is finitely generated and free. The proof is based on the 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.
Keywords: total coordinate ring, Cox ring, algebraic variety, factorial ring, graded factoriality, divisor class group, torsion, Weil divisor, Cartier divisor.
Received: 05.02.2008
English version:
Mathematical Notes, 2009, Volume 85, Issue 5, Pages 623–629
DOI: https://doi.org/10.1134/S0001434609050022
Bibliographic databases:
UDC: 512.71
Language: Russian
Citation: I. V. Arzhantsev, “On the Factoriality of Cox rings”, Mat. Zametki, 85:5 (2009), 643–651; Math. Notes, 85:5 (2009), 623–629
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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