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

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

Caveat

The ordering of the list L must correspond to the ordering of the rays of the fan output by raySortOfFan.

See also

Ways to use twist:

  • twist(ToricVectorBundleKlyachko,List)

For the programmer

The object twist is a method function.

The source of this document is in ToricVectorBundles.m2:3872:0.