determinant(AbstractSheaf) -- determinant of an abstract sheaf

Synopsis

Usage:
det F
Function: determinant
Inputs:
- F, an abstract sheaf
Optional inputs:
- Strategy => ..., -- choose between Bareiss and Cofactor algorithms
Outputs:
- an abstract sheaf, the determinant of F

Description

The determinant of F is the n-th exterior power of F, where n is the rank of F.

i1 : X = PP^1

o1 = X

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

i2 : F = OO_X(1) ++ OO_X(1) ++ OO_X(3)

o2 = F

o2 : an abstract sheaf of rank 3 on X

i3 : det F

o3 = a sheaf

o3 : an abstract sheaf of rank 1 on X

i4 : chern oo

o4 = 1 + 5H
           2,1

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

i5 : rank ooo

o5 = 1

determinant(AbstractSheaf) -- determinant of an abstract sheaf

Synopsis

Description

See also