If F or G is a ring element of degree 0, it represents a trivial bundle of that rank.
i1 : X = abstractProjectiveSpace 1 o1 = X o1 : a flag bundle with subquotient ranks {2:1} |
i2 : OO_X(1) * OO_X(2) o2 = a sheaf o2 : an abstract sheaf of rank 1 on X |
i3 : chi oo o3 = 4 |
The sheaves can be on different varieties if one of the varieties is over the other.