sectionZeroLocus(AbstractSheaf)

Synopsis

Usage:
sectionZeroLocus F
Function: sectionZeroLocus
Inputs:
- F, an abstract sheaf
Outputs:
- an abstract variety, the zero locus of a generic section of F

Description

i1 : X = base(5, n, Bundle => (E,3,c), Bundle => (T,5,t), Bundle => (L,1,{h}))

o1 = X

o1 : an abstract variety of dimension 5

i2 : X.TangentBundle = T

o2 = T

o2 : an abstract sheaf of rank 5 on X

i3 : Y = sectionZeroLocus E

o3 = Y

o3 : an abstract variety of dimension 2

i4 : Y.TautologicalLineBundle = OO_Y(h)

o4 = a sheaf

o4 : an abstract sheaf of rank 1 on Y

i5 : chern tangentBundle Y

                         2
o5 = 1 + (- c  + t ) + (c  - c t  - c  + t )
             1    1      1    1 1    2    2

o5 : QQ[n, c , c , c , t , t , t , t , t , h][]
            1   2   3   1   2   3   4   5

i6 : integral oo

               2
o6 = integral(c c  - c c t  - c c  + c t )
               1 3    1 3 1    2 3    3 2

o6 : Expression of class Adjacent

i7 : chi ((tangentBundle Y)(n))

               2   2                         1 2     3         7   2   5       5
o7 = integral(n c h  - 2n*c c h + 2n*c t h + -c c  - -c c t  + -c t  + -c c  - -c t )
                 3         1 3        3 1    3 1 3   2 1 3 1   6 3 1   6 2 3   6 3 2

o7 : Expression of class Adjacent

Caveat

The intersection ring provided for the zero locus contains only those classes arising by pull-back from the ambient variety: there is no algorithm to compute the intersection ring.