base -- the basis matrices for the rays

Synopsis

• Usage:

  b = base E

• Inputs:
  • E, a vector bundle on a toric variety (Klyachko's description)
• Outputs:
  • b, a hash table

Description

The basis of a toric vector bundle in Klyachko's description is given for each ray as a square matrix of rank $k$ of the bundle. The output is a HashTable where the keys are the rays of the fan given as one column matrices over ZZ, and for each ray a $k$ by $k$ matrix over QQ and $k$ is the rank of the bundle.

i1 : E = tangentBundle hirzebruchFan 3

o1 = {dimension of the variety => 2 }
      number of affine charts => 4
      number of rays => 4
      rank of the vector bundle => 2

o1 : ToricVectorBundleKlyachko

i2 : base E

o2 = HashTable{| -1 | => | -1 1/3 |}
               | 3  |    | 3  0   |
               | 0  | => | 0  1 |
               | -1 |    | -1 0 |
               | 0 | => | 0 1 |
               | 1 |    | 1 0 |
               | 1 | => | 1 0 |
               | 0 |    | 0 1 |

o2 : HashTable

See also

• addBase -- changing the basis matrices of a toric vector bundle in Klyachko's description
• filtration -- the filtration matrices of the vector bundle
• isVectorBundle -- checks if the data does in fact define an equivariant toric vector bundle