The category of coherent sheaves on a normal toric variety is equivalent to the quotient category of finitely generated modules over the total coordinate ring by the full subcategory of torsion modules with respect to the irrelevant ideal. In particular, the total coordinate ring corresponds to the structure sheaf.
On projective space, we can make the structure sheaf in a few ways.
i1 : PP3 = projectiveSpace 3;
|
i2 : F = sheaf(PP3, ring PP3)
o2 = OO
PP3
o2 : SheafOfRings
|
i3 : G = sheaf PP3
o3 = OO
PP3
o3 : SheafOfRings
|
i4 : F === G
o4 = true
|
i5 : H = OO_PP3
o5 = OO
PP3
o5 : SheafOfRings
|
i6 : F === H
o6 = true
|