Accepts both Grothendieck-style and Fulton-style ${\mathbb P}(E)$, but in the case a decision cannot be made based on ranks (i.e. when $E$ has rank $2$), defaults to Fulton-style notation (so ${\mathbb P}(E)$ is the space of sub-line-bundles of $E$).
Does not check whether $L$ is basepoint-free. Weird results are probably possible if $L$ is not.
i1 : X = flagBundle({2,2}) --the Grassmannian GG(1,3) o1 = X o1 : a flag bundle with subquotient ranks {2:2} |
i2 : (S,Q) = bundles X o2 = (S, Q) o2 : Sequence |
i3 : L = exteriorPower(2,dual S) o3 = L o3 : an abstract sheaf of rank 1 on X |
i4 : P = flagBundle({5,1}) --Grothendieck-style PP^5 o4 = P o4 : a flag bundle with subquotient ranks {5, 1} |
i5 : f = map(P,X,L) -- Plucker embedding of GG(1,3) in PP^5 o5 = f o5 : a map to P from X |
i6 : H = last bundles P o6 = H o6 : an abstract sheaf of rank 1 on P |
i7 : f^* (chern(1,H)) -- hyperplane section, should be sigma_1 o7 = H 2,1 QQ[][H ..H ] 1,1 2,2 o7 : --------------------------------------------------------------------------- (- H - H , - H - H H - H , - H H - H H , -H H ) 1,1 2,1 1,2 1,1 2,1 2,2 1,2 2,1 1,1 2,2 1,2 2,2 |
i8 : f_* chern(0,S) --expect 2 times hyperplane class since GG(1,3) has degree 2 o8 = 2H 2,1 QQ[][H ..H , H ] 1,1 1,5 2,1 o8 : ------------------------------------------------------------------------------------------------------ (- H - H , - H - H H , - H - H H , - H - H H , - H - H H , -H H ) 1,1 2,1 1,2 1,1 2,1 1,3 1,2 2,1 1,4 1,3 2,1 1,5 1,4 2,1 1,5 2,1 |