David A. Cox introduced the total coordinate ring S of a normal toric variety X and the irrelevant ideal B. The polynomial ring S has one variable for each ray in the associated fan and a natural grading by the class group. The monomial ideal B encodes the maximal cones. The following results of Cox indicate the significance of the pair (S,B).
In particular, we may represent any coherent sheaf on X by giving a finitely generated graded S-module.
The following methods allow one to make and manipulate coherent sheaves on normal toric varieties.