The list r of ranks can be obtained later with F.BundleRanks, see BundleRanks. Its sum can be obtained with F.Rank.
The list of consecutive quotients in the tautological filtration can be obtained later with bundles F, see bundles. See also SubBundles and QuotientBundles.
The (relative) tautological line bundle can be obtained later with OOF(1).
The structure map from F to the variety of E can be obtained later with F.StructureMap, see StructureMap. Abstract sheaves and cycle classes can be pulled back and pushed forward, see AbstractVarietyMap ^* and AbstractVarietyMap _*. Integration will work if it works on the variety of E, see integral. The (relative) tangent bundle can be obtained from it, see tangentBundle(AbstractVarietyMap).
i1 : base(3,Bundle => (E,4,c)) o1 = a variety o1 : an abstract variety of dimension 3 |
i2 : F = flagBundle({2,2},E) o2 = F o2 : a flag bundle with subquotient ranks {2:2} |
i3 : bundles F o3 = (a sheaf, a sheaf) o3 : Sequence |
i4 : rank \ oo o4 = (2, 2) o4 : Sequence |
i5 : chern \ ooo 2 o5 = (1 + (- H + c ) + (H - H - c H + c ), 1 + H + H ) 2,1 1 2,1 2,2 1 2,1 2 2,1 2,2 o5 : Sequence |
i6 : product toList oo o6 = 1 + c + c + c 1 2 3 QQ[c , c , c ][H , H , H , H ] 1 2 3 1,1 1,2 2,1 2,2 o6 : ------------------------------------------------------------------------------------------ (- H - H + c , - H - H H - H + c , - H H - H H + c , -H H ) 1,1 2,1 1 1,2 1,1 2,1 2,2 2 1,2 2,1 1,1 2,2 3 1,2 2,2 |
i7 : intersectionRing flagBundle({2,2},E,VariableNames=>{{a,b},t}) QQ[c , c , c ][a, b, t , t ] 1 2 3 1 2 o7 = ---------------------------------------------------------------- (- a - t + c , - b - a*t - t + c , - b*t - a*t + c , -b*t ) 1 1 1 2 2 1 2 3 2 o7 : QuotientRing |