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# exceptionalDivisor -- get the exceptional divisor of a blowup

- Usage:
    `exceptionalDivisor X`
- Inputs:
  - X, an abstract variety, a blowup, built using blowup
- Outputs:
  - an abstract sheaf, the exceptional divisor on X, expressed as a line bundle

## Description

    i1 : T = abstractProjectiveSpace 2

    o1 = T

    o1 : a flag bundle with subquotient ranks {1..2}

    i2 : S = abstractProjectiveSpace 0

    o2 = S

    o2 : a flag bundle with subquotient ranks {1, 0}

    i3 : i = map(T,S,OO_S) -- inclusion of a point in P^2

    o3 = i

    o3 : a map to T from S

    i4 : X = first blowup(i)

    o4 = X

    o4 : an abstract variety of dimension 2

    i5 : exceptionalDivisor X

    o5 = a sheaf

    o5 : an abstract sheaf of rank 1 on X

    i6 : chern oo

    o6 = 1 + E
              0

                   QQ[][h, H   ..H   ]
                            2,1   2,2
         --------------------------------------[E ]
         (- h - H   , - h*H    - H   , -h*H   )  0
                 2,1       2,1    2,2      2,2
    o6 : ------------------------------------------
                               2
                     (H   E , E  + H   )
                       2,1 0   0    2,2

## See also

- blowup -- blow up an abstract variety along a subvariety

## Ways to use exceptionalDivisor:

- `exceptionalDivisor(AbstractVariety)`

## For the programmer

The object exceptionalDivisor is a method function.

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