QuotientBundles -- get the quotient bundles of the tautological filtration on a flag bundle

Synopsis

Usage:

F.QuotientBundles
Inputs:
- F, an abstract flag bundle,
Outputs:
- a list $\{E_n/E_n, E_n/E_{n-1}, ..., E_n/E_1, E_n/E_0\}$ whose elements are the quotient bundles in the tautological filtration $0 = E_0 \subseteq{} E_1 \subseteq{} ... \subseteq{} E_n = f^* B$, 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.QuotientBundles

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

o2 : List

i3 : rank \ oo

o3 = {0, 2, 3, 4}

o3 : List

i4 : netList \\ chern \ ooo

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

Functions with optional argument named QuotientBundles :

flagBundle(...,QuotientBundles=>...) -- see flagBundle -- make a flag bundle

For the programmer

The object QuotientBundles is a symbol.