Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On factoriality of Cox rings   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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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat