For a given pure, full dimensional and pointed Fan
F the
function
toricVectorBundle generates the trivial toric vector bundle of rank
k.
"If no further options are given then the resulting bundle will be in Klyachko’s description:
The basis assigned to every ray is the standard basis of
ℚk and the filtration
is given by
0 for all
i<0 and
ℚk
for
i>=0."
i1 : E = toricVectorBundle(2,projectiveSpaceFan 2)
o1 = {dimension of the variety => 2 }
number of affine charts => 3
number of rays => 3
rank of the vector bundle => 2
o1 : ToricVectorBundleKlyachko
|
i2 : details E
o2 = HashTable{| -1 | => (| 1 0 |, 0)}
| -1 | | 0 1 |
| 0 | => (| 1 0 |, 0)
| 1 | | 0 1 |
| 1 | => (| 1 0 |, 0)
| 0 | | 0 1 |
o2 : HashTable
|
If the option
"Type" => "Kaneyama" is given then the resulting bundle will be in
Kaneyama's description: The degree vectors of this bundle are all zero vectors and the transition matrices
are all the identity. Note that for Kaneyama's description only complete, pointed fans are implemented and
thus a non complete fan will produce an error.
i3 : E = toricVectorBundle(2,pp1ProductFan 2,"Type" => "Kaneyama")
o3 = {dimension of the variety => 2 }
number of affine charts => 4
rank of the vector bundle => 2
o3 : ToricVectorBundleKaneyama
|
i4 : details E
o4 = (HashTable{0 => (| 1 0 |, 0) }, HashTable{(0, 1) => | 1 0 |})
| 0 1 | | 0 1 |
1 => (| 1 0 |, 0) (0, 2) => | 1 0 |
| 0 -1 | | 0 1 |
2 => (| -1 0 |, 0) (1, 3) => | 1 0 |
| 0 1 | | 0 1 |
3 => (| -1 0 |, 0) (2, 3) => | 1 0 |
| 0 -1 | | 0 1 |
o4 : Sequence
|