segre(AbstractSheaf) -- compute the total Segre class of a sheaf

Synopsis

• Function: segre

• Usage:

  segre A

• Inputs:
  • A, an abstract sheaf
• Outputs:
  • a ring element, the total Segre class of A, defined as the reciprocal of the chern class of the dual of A. (In a future version, the dual may be omitted, and an alternative function segre' may be introduced.)

Description

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

o1 = a variety

o1 : an abstract variety of dimension 4

i2 : chern B

o2 = 1 + b  + b  + b
          1    2    3

o2 : QQ[b ..b ]
         1   3

i3 : segre B

                2           3                   4     2      2
o3 = 1 + b  + (b  - b ) + (b  - 2b b  + b ) + (b  - 3b b  + b  + 2b b )
          1     1    2      1     1 2    3      1     1 2    2     1 3

o3 : QQ[b ..b ]
         1   3

See also

• chern -- compute Chern classes of a sheaf