Cox ring

Short description: Universal homogenous coordinate ring of a projectile variety

In algebraic geometry, a Cox 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 Keel), based on an earlier construction by David A. Cox in 1995 for toric varieties.

References

• Cox, David A. (1995), "The homogeneous coordinate ring of a toric variety", J. Algebraic Geom. 4 (1): 17–50 
• Hu, Yi; Keel, Sean (2000), "Mori dream spaces and GIT", Michigan Math. J. 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