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# AbstractVarietyMap _* -- push forward operator associated to a map of varieties

- Operator: _*
- Usage:
    `f_*`
- Inputs:
  - f, an abstract variety map,
- Outputs:
  - a function, the push forward operator associated to f, a function that can be applied to an abstract sheaf or a cycle class

## Description

    i1 : X = abstractProjectiveSpace' 4

    o1 = X

    o1 : a flag bundle with subquotient ranks {4, 1}

    i2 : f = X.StructureMap

    o2 = f

    o2 : a map to point from X

    i3 : OO_X(1)

    o3 = a sheaf

    o3 : an abstract sheaf of rank 1 on X

    i4 : f_* oo

    o4 = a sheaf

    o4 : an abstract sheaf of rank 5 on point

    i5 : ch OO_X(1)

                 1 2   1 3    1 4
    o5 = 1 + h + -h  + -h  + --h
                 2     6     24

                                  QQ[][H   ..H   , h]
                                        1,1   1,4
    o5 : --------------------------------------------------------------------
         (- H    - h, - H    - H   h, - H    - H   h, - H    - H   h, -H   h)
             1,1         1,2    1,1      1,3    1,2      1,4    1,3     1,4

    i6 : f_* oo

          1
    o6 = --
         24

    o6 : QQ[]

## See also

- integral -- compute an integral (push forward a cycle to the base)
- AbstractVarietyMap ^* -- pull back operator associated to a map of varieties

## Ways to use this method:

- AbstractVarietyMap _* -- push forward operator associated to a map of varieties

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Schubert2.m2:1857:0.