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

Usage:

g = graphToricChernCharacter E
Inputs:
- E, a vector bundle on a toric variety (Klyachko's description)
Outputs:
- g, a hash table, whose keys are curve cones and the value of a key is a pair of the connected components
Consequences:
- The result of graphToricChernCharacter will be stored as a cacheValue (missing documentation) in E.cache#graphToricChernCharacter. It will be used by other methods.

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

o2 : HashTable

i3 : g = graphToricChernCharacter E

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

o3 : HashTable

Ways to use graphToricChernCharacter:

graphToricChernCharacter(ToricVectorBundleKlyachko)

For the programmer

The object graphToricChernCharacter is a method function with options.

The source of this document is in PositivityToricBundles.m2:1079:0.

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

Description

See also

Ways to use graphToricChernCharacter:

For the programmer