ctop(AbstractSheaf) -- the top Chern class of an abstract sheaf

Synopsis

Usage:
ctop F
Function: ctop
Inputs:
- F, an abstract sheaf
Outputs:
- a ring element, the top Chern class of F

Description

Here we compute the top Chern class of a vector bundle of rank 6 on the way toward getting the number of lines on quintic threefold.

i1 : G = flagBundle{3,2}

o1 = G

o1 : a flag bundle with ranks {3, 2}

i2 : B = symmetricPower_5 last bundles G

o2 = B

o2 : an abstract sheaf of rank 6 on G

i3 : ctop B

          3
o3 = 2875H
          2,2

                                    QQ[][H   , H   , H   , H   , H   ]
                                          1,1   1,2   1,3   2,1   2,2
o3 : ------------------------------------------------------------------------------------------------
     (H    + H   , H    + H   H    + H   , H    + H   H    + H   H   , H   H    + H   H   , H   H   )
       1,1    2,1   1,2    1,1 2,1    2,2   1,3    1,2 2,1    1,1 2,2   1,3 2,1    1,2 2,2   1,3 2,2

i4 : degree oo

o4 = {6}

o4 : List

i5 : integral ooo

o5 = 2875