tangentBundle -- get the tangent bundle

Usage:

tangentBundle X

tangentBundle f
Inputs:
- X, an abstract variety,
- f, an abstract variety map,
Outputs:
- an abstract sheaf, the (absolute) tangent bundle of $X$ or the (relative) tangent bundle of $f$

Description

i1 : X = abstractProjectiveSpace' 2

o1 = X

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

i2 : Y = abstractProjectiveSpace'_2 X

o2 = Y

o2 : a flag bundle with subquotient ranks {2, 1}

i3 : tangentBundle Y

o3 = a sheaf

o3 : an abstract sheaf of rank 4 on Y

i4 : chern oo

                        2            2         2     2       2 2
o4 = 1 + (3h + 3h) + (3h  + 9h*h + 3h ) + (9h*h  + 9h h) + 9h h

              QQ[][H   ..H   , h]
                    1,1   1,2
     ------------------------------------[H   ..H   , h]
     (- H    - h, - H    - H   h, -H   h)  1,1   1,2
         1,1         1,2    1,1     1,2
o4 : ---------------------------------------------------
             (- H    - h, - H    - H   h, -H   h)
                 1,1         1,2    1,1     1,2

i5 : tangentBundle Y.StructureMap

o5 = a sheaf

o5 : an abstract sheaf of rank 2 on Y

i6 : chern oo

                2
o6 = 1 + 3h + 3h

              QQ[][H   ..H   , h]
                    1,1   1,2
     ------------------------------------[H   ..H   , h]
     (- H    - h, - H    - H   h, -H   h)  1,1   1,2
         1,1         1,2    1,1     1,2
o6 : ---------------------------------------------------
             (- H    - h, - H    - H   h, -H   h)
                 1,1         1,2    1,1     1,2

Ways to use tangentBundle:

tangentBundle(AbstractVariety)
tangentBundle(AbstractVarietyMap)

For the programmer

The object tangentBundle is a method function.

The source of this document is in Schubert2.m2:1857:0.

tangentBundle -- get the tangent bundle

Description

See also

Ways to use tangentBundle:

For the programmer