In algebraic geometry, the homogeneous coordinate ring R of an algebraic variety V given as a subvariety of projective space of a given dimension N is...

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...

multiplication may not be commutative. For the general ring A, a projective line over A can be defined with homogeneous factors acting on the left and the projective...

] / I {\displaystyle k[x_{0},\ldots ,x_{n}]/I} is called the homogeneous coordinate ring of X. Basic invariants of X such as the degree and the dimension...

between homogeneous polynomials and projective varieties (cf. Homogeneous coordinate ring.) The above definitions have been generalized to rings graded...

homogeneous coordinate system is one where only the ratios of the coordinates are significant and not the actual values. Some other common coordinate...

For a projective variety, there is an analogous ring called the homogeneous coordinate ring. Those rings are essentially the same things as varieties: they...

transform. The goal of the theory is to prove results on the homogeneous coordinate ring of the embedded abelian variety A, that is, set in a projective...

curve, then the canonical ring is again the homogeneous coordinate ring of the image of the canonical map. In general, if the ring above is finitely generated...

function on X is of the form g/h for some homogeneous elements g, h of the same degree in the homogeneous coordinate ring k [ X ¯ ] {\displaystyle k[{\overline...