SubBundles -- get the subbundles of the tautological filtration on a flag bundle

Synopsis

Usage:

F.SubBundles
Inputs:
- F, an abstract flag bundle
Outputs:
- a list whose elements are the subbundles $0 = E_0 \subseteq{} E_1 \subseteq{} ... \subseteq{} E_n = f^* B$ in the tautological filtration of $f^* B$, where $F$ is a flag bundle parametrizing filtrations of an abstract sheaf $B$ on a variety $X$, and $f : F \rightarrow X$ is the structure map of $F$

Description

i1 : F = flagBundle {1,1,2}

o1 = F

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

i2 : F.SubBundles

o2 = {a sheaf, a sheaf, a sheaf, a sheaf}

o2 : List

i3 : rank \ oo

o3 = {0, 1, 2, 4}

o3 : List

i4 : netList \\ chern \ ooo

     +------------------------+
o4 = |1                       |
     +------------------------+
     |1 + (- H    - H   )     |
     |        2,1    3,1      |
     +------------------------+
     |             2          |
     |1 - H    + (H    - H   )|
     |     3,1     3,1    3,2 |
     +------------------------+
     |1                       |
     +------------------------+

For the programmer

The object SubBundles is a symbol.