> proj(4,h,tang): # need tangentbundle for chi
i1 : X = projectiveSpace'(4,base n,VariableName => h) o1 = X o1 : a flag bundle with subquotient ranks {4, 1} |
> F:=sheaf(2,[5*h,10*h^2]): # defines the Horrocks-Mumford bundle
i2 : F = abstractSheaf(X, Rank => 2, ChernClass => 1 + 5*h + 10*h^2) o2 = F o2 : an abstract sheaf of rank 2 on X |
> chi(F&*o(n*h)); # computes chi of its twists 4 3 125 2 1/12 n + 5/3 n + --- n + 125/6 n + 2 12
i3 : chi (F ** OO(n*h)) 1 4 5 3 125 2 125 o3 = --n + -n + ---n + ---n + 2 12 3 12 6 o3 : QQ[n] |