F-G
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 0 on X
i3 : chi oo o3 = -1
The sheaves can be on different varieties if one of the varieties is over the other.