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PositivityToricBundles :: graphToricChernCharacter

graphToricChernCharacter -- computes the lines connected the components of the toric Chern character of a toric vector bundle

Synopsis

Description

Given a toric vector bundle in Klyachko's description, graphToricChernCharacter connects the component of its toric Chern character.
graphToricChernCharacter calls internally the method toricChernCharacter.
i1 : E = tangentBundle(projectiveSpaceFan 2)

o1 = {dimension of the variety => 2 }
      number of affine charts => 3
      number of rays => 3
      rank of the vector bundle => 2

o1 : ToricVectorBundleKlyachko
i2 : c = toricChernCharacter E

o2 = HashTable{| -1 0 | => {| 1 |, | 1  |}}
               | -1 1 |     | 0 |  | -1 |
               | 1 -1 | => {| -1 |, | 0 |}
               | 0 -1 |     | 1  |  | 1 |
               | 1 0 | => {| -1 |, | 0  |}
               | 0 1 |     | 0  |  | -1 |

o2 : HashTable
i3 : g = graphToricChernCharacter E

o3 = HashTable{| -1 | => {{| -1 |, | 1  |}, {| 0 |, | 1 |}}}
               | -1 |      | 1  |  | -1 |    | 1 |  | 0 |
               | 0 | => {{| 1 |, | -1 |}, {| 1  |, | 0  |}}
               | 1 |      | 0 |  | 0  |    | -1 |  | -1 |
               | 1 | => {{| -1 |, | -1 |}, {| 0 |, | 0  |}}
               | 0 |      | 1  |  | 0  |    | 1 |  | -1 |

o3 : HashTable

See also

Ways to use graphToricChernCharacter :

For the programmer

The object graphToricChernCharacter is a method function with options.