exteriorPower(ZZ,ToricVectorBundle) -- the 'l'-th exterior power of a toric vector bundle

Synopsis

• Function: exteriorPower

• Usage:

  Ee = exteriorPower(l,E)

• Inputs:
  • l, an integer, strictly positive
  • E, an instance of the type ToricVectorBundle
• Optional inputs:
  • Strategy => ..., default value null,
• Outputs:
  • Ee, an instance of the type ToricVectorBundle

Description

exteriorPower computes the l-th exterior power of a toric vector bundle in each description. The resulting bundle will be given in the same description as the original bundle. l must be strictly positive and at most equal 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 : details E

o2 = HashTable{| -1 | => (| -1 1/3 |, | -1 0 |)}
               | 3  |     | 3  0   |
               | 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 : Ee = exteriorPower(2,E)

o3 = {dimension of the variety => 2 }
      number of affine charts => 4
      number of rays => 4
      rank of the vector bundle => 1

o3 : ToricVectorBundleKlyachko

i4 : details Ee

o4 = HashTable{| -1 | => (| -1 |, | -1 |)}
               | 3  |
               | 0  | => (| 1 |, | -1 |)
               | -1 |
               | 0 | => (| -1 |, | -1 |)
               | 1 |
               | 1 | => (| 1 |, | -1 |)
               | 0 |

o4 : HashTable

See also

• ToricVectorBundle ++ ToricVectorBundle -- the direct sum of two toric vector bundles
• tensor(ToricVectorBundle,ToricVectorBundle) -- the tensor product of two toric vector bundles
• symmetricPower(ZZ,ToricVectorBundle) -- the 'l'-th symmetric power of a toric vector bundle