AbstractVarietyMap ^* -- pull back operator associated to a map of varieties

Synopsis

• Usage:
f^*
• Operator: ^*
• Inputs:
• f,
• Outputs:
• , the pull back operator associated to f, a function that can be applied to an abstract sheaf or a cycle class

Description

 ```i1 : S = base(4, Bundle => (E,4,c) ) o1 = S o1 : an abstract variety of dimension 4``` ```i2 : X = flagBundle( {2,2}, E ) o2 = X o2 : a flag bundle with ranks {2, 2}``` ```i3 : f = X.StructureMap o3 = f o3 : a map to S from X``` ```i4 : chern E o4 = 1 + c + c + c + c 1 2 3 4 o4 : QQ[c , c , c , c ] 1 2 3 4``` ```i5 : f^* oo o5 = 1 + c + c + c + c 1 2 3 4 QQ[c , c , c , c ][H , H , H , H ] 1 2 3 4 1,1 1,2 2,1 2,2 o5 : ---------------------------------------------------------------------------------------- (H + H - c , H + H H + H - c , H H + H H - c , H H - c ) 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 4``` ```i6 : f^* E o6 = a sheaf o6 : an abstract sheaf of rank 4 on X``` ```i7 : chern oo o7 = 1 + c + c + c + c 1 2 3 4 QQ[c , c , c , c ][H , H , H , H ] 1 2 3 4 1,1 1,2 2,1 2,2 o7 : ---------------------------------------------------------------------------------------- (H + H - c , H + H H + H - c , H H + H H - c , H H - c ) 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 4```