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# projectiveBundle' -- make a projective bundle from an abstract sheaf

- Usage:
    `projectiveBundle' F`
    `projectiveBundle'(n,X)`
    `projectiveBundle' n`
- Inputs:
  - F, an abstract sheaf,
  - n, an integer,
  - X, an abstract variety,
- Optional inputs:
  - VariableNames => a thing, default value null, see flagBundle(...,VariableNames=>...)
- Outputs:
  - the projective bundle of rank 1 quotient bundles of the abstract sheaf $F$. If $F$ is omitted, then a projective space of dimension $n$ over $X$ is produced. If $X$ is omitted, then point is used as the base.

## Description

    i1 : X = projectiveBundle' 4

    o1 = X

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

    i2 : F = OO_X(2) ++ OO_X(3) ++ OO_X(4)

    o2 = F

    o2 : an abstract sheaf of rank 3 on X

    i3 : Y = projectiveBundle' F

    o3 = Y

    o3 : a flag bundle with subquotient ranks {2, 1}

    i4 : dim Y

    o4 = 6

    i5 : integral (chern_1 OO_Y(1))^(dim Y)

    o5 = 1351

    i6 : bundles X/rank

    o6 = (4, 1)

    o6 : Sequence

## Caveat

Perhaps this should be merged with abstractProjectiveSpace. (The optional arguments are slightly different.)

## See also

- projectiveBundle -- make a projective bundle from an abstract sheaf
- abstractProjectiveSpace -- make a projective space
- flagBundle -- make a flag bundle

## Ways to use projectiveBundle':

- `projectiveBundle'(AbstractSheaf)`
- `projectiveBundle'(ZZ)`
- `projectiveBundle'(ZZ,AbstractVariety)`

## For the programmer

The object projectiveBundle' is a method function with options.

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