Cox ring
From HandWiki
Short description: Universal homogenous coordinate ring of a projective variety
In algebraic geometry, a Cox ring (or total coordinate ring) is a sort of universal homogeneous coordinate ring for a projective variety, and is (roughly speaking) a direct sum of the spaces of sections of all isomorphism classes of line bundles.
Cox rings were introduced by Hu and Keel in 2000,[1] based on an earlier construction by David A. Cox in 1995 for toric varieties.[2]
Notes
References
- Cox, David A. (1995), "The homogeneous coordinate ring of a toric variety", Journal of Algebraic Geometry 4 (1): 17–50
- Hu, Yi; Keel, Sean (2000), "Mori dream spaces and GIT", Michigan Mathematical Journal 48: 331–348, doi:10.1307/mmj/1030132722
- Arzhantsev, Ivan; Derenthal, Ulrich; Hausen, Jürgen; Laface, Antonio (2015), Cox Rings, Cambridge Studies in Advanced Mathematics, 144 (1st ed.), Cambridge: Cambridge University Press, ISBN 978-1-107-02462-5
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