twist -- twists a toric vector bundle with a line bundle

Synopsis

• Usage:

  E1 = twist(E,L)

• Inputs:
  • E, a vector bundle on a toric variety (Klyachko's description)
  • L, a list
• Outputs:
  • E1, a vector bundle on a toric variety (Klyachko's description)

Description

twist takes a toric vector bundle $E$ in Klyachko's description and a list of integers L. The list must contain one entry for each ray of the underlying fan. Then it computes the twist of the vector bundle by the line bundle given by these integers (see weilToCartier).

i1 : E = tangentBundle hirzebruchFan 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 : L = {1,-2,3,-4}

o2 = {1, -2, 3, -4}

o2 : List

i3 : E1 = twist(E,L)

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 | => (| -1 1/2 |, | -4 -3 |)}
               | 2  |     | 2  0   |
               | 0  | => (| 0  1 |, | -2 -1 |)
               | -1 |     | -1 0 |
               | 0 | => (| 0 1 |, | 1 2 |)
               | 1 |     | 1 0 |
               | 1 | => (| 1 0 |, | 3 4 |)
               | 0 |     | 0 1 |

o4 : HashTable

See also

• weilToCartier -- the line bundle given by a Cartier divisor
• cartierIndex -- the Cartier index of a Weil divisor
• details -- the details of a toric vector bundle