# Lines on a quintic threefold. This is the top Chern class of the # 5th symmetric power of the universal quotient bundle on the Grassmannian # of lines. > > grass(2,5,c): # Lines in P^4.
i1 : Gc = flagBundle({3,2}, VariableNames => {,c}) o1 = Gc o1 : a flag bundle with subquotient ranks {3, 2} |
i2 : (Sc,Qc) = bundles Gc o2 = (Sc, Qc) o2 : Sequence |
> B:=symm(5,Qc): # Qc is the rank 2 quotient bundle, B its 5th > # symmetric power.
i3 : B = symmetricPower(5,Qc) o3 = B o3 : an abstract sheaf of rank 6 on Gc |
> c6:=chern(rank(B),B):# the 6th Chern class of this rank 6 bundle.
i4 : c6 = chern(rank B,B) 3 o4 = 2875c 2 QQ[][H ..H , c ..c ] 1,1 1,3 1 2 o4 : ----------------------------------------------------------------------------------------- (- H - c , - H - H c - c , - H - H c - H c , - H c - H c , -H c ) 1,1 1 1,2 1,1 1 2 1,3 1,2 1 1,1 2 1,3 1 1,2 2 1,3 2 |
> integral(c6); 2875
i5 : integral c6 o5 = 2875 |