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The phrase "a sort of universal homogeneous coordinate ring" is somewhat informal and might be misleading. To me "A is a sort of B" conveys either, formally, that A is a subset of B or informally, that A is akin to or analogous to B. Here I think that Cox ring is best described as a generalisation of the homogeneous coordinate ring, with a universal property. Is it synonymous with total coordinate ring in Hu and Keel (see Cox et al, "Toric varieties", 2011)? If so, should be worth mentioning. Deltahedron ( talk) 07:33, 28 February 2014 (UTC)
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The phrase "a sort of universal homogeneous coordinate ring" is somewhat informal and might be misleading. To me "A is a sort of B" conveys either, formally, that A is a subset of B or informally, that A is akin to or analogous to B. Here I think that Cox ring is best described as a generalisation of the homogeneous coordinate ring, with a universal property. Is it synonymous with total coordinate ring in Hu and Keel (see Cox et al, "Toric varieties", 2011)? If so, should be worth mentioning. Deltahedron ( talk) 07:33, 28 February 2014 (UTC)