chern(ZZ,ZZ,AbstractSheaf) -- compute several Chern classes of an abstract sheaf

Synopsis

Function: chern
Usage:

chern(n,m,A)
Inputs:
- n, an integer,
- m, an integer,
- A, an abstract sheaf,
Outputs:
- a list, the list $ \{ c_n A .. c_m A \} $ of Chern classes of $A$

Description

In the following example, we consider two vector bundles A and B of ranks 2 and 3 on a variety of dimension 4.

i1 : base(4,Bundle => (A,2,a), Bundle => (B,3,b))

o1 = a variety

o1 : an abstract variety of dimension 4

i2 : netList chern(2,4,B-A)

     +-----------------------------------------------------+
     | 2                                                   |
o2 = |a  - a  - a b  + b                                   |
     | 1    2    1 1    2                                  |
     +-----------------------------------------------------+
     |   3            2                                    |
     |- a  + 2a a  + a b  - a b  - a b  + b                |
     |   1     1 2    1 1    2 1    1 2    3               |
     +-----------------------------------------------------+
     | 4     2      2    3                2                |
     |a  - 3a a  + a  - a b  + 2a a b  + a b  - a b  - a b |
     | 1     1 2    2    1 1     1 2 1    1 2    2 2    1 3|
     +-----------------------------------------------------+

Ways to use this method: