randomDeformation -- a random deformation of a given toric vector bundle
Synopsis
-
- Usage:
E1 = randomDeformation(E,h)
E1 = randomDeformation(E,l,h)
-
Inputs:
-
Outputs:
Description
"For a bundle of rank $k$ the function "
randomDeformation" replaces each base matrix by a random $k$ by $k$ matrix with entries between $l$ and $h$. For this $h$ must be greater than $l$. If $l$ is not given then the random entries are between $0$ and $h$ and then $h$ must be strictly positive."
i1 : E = tangentBundle pp1ProductFan 2
o1 = {dimension of the variety => 2 }
number of affine charts => 4
number of rays => 4
rank of the vector bundle => 2
o1 : ToricVectorBundleKlyachko
|
i2 : details E
o2 = HashTable{| -1 | => (| -1 0 |, | -1 0 |)}
| 0 | | 0 1 |
| 0 | => (| 0 1 |, | -1 0 |)
| -1 | | -1 0 |
| 0 | => (| 0 1 |, | -1 0 |)
| 1 | | 1 0 |
| 1 | => (| 1 0 |, | -1 0 |)
| 0 | | 0 1 |
o2 : HashTable
|
i3 : E1 = randomDeformation(E,-2,6)
o3 = {dimension of the variety => 2 }
number of affine charts => 4
number of rays => 4
rank of the vector bundle => 2
o3 : ToricVectorBundleKlyachko
|
i4 : details E1
o4 = HashTable{| -1 | => (| 6 1 |, | -1 0 |) }
| 0 | | 1 5 |
| 0 | => (| 6 -1 |, | -1 0 |)
| -1 | | 1 5 |
| 0 | => (| 6 3 |, | -1 0 |)
| 1 | | 0 1 |
| 1 | => (| 6 6 |, | -1 0 |)
| 0 | | 3 5 |
o4 : HashTable
|
Caveat
In general, randomDeformation will only produce a reflexive sheaf, not a locally free one. However, for smooth toric surfaces, equivariant reflexive sheaves are automatically locally free.
See also
-
base -- the basis matrices for the rays
-
filtration -- the filtration matrices of the vector bundle
-
details -- the details of a toric vector bundle
-
isGeneral -- checks whether a toric vector bundle is general
Ways to use randomDeformation:
-
randomDeformation(ToricVectorBundleKlyachko,ZZ)
-
randomDeformation(ToricVectorBundleKlyachko,ZZ,ZZ)