next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
NormalToricVarieties :: Total coordinate rings and coherent sheaves

Total coordinate rings and coherent sheaves

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.

Menu

See also