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

## Synopsis

• Usage:
g = graphToricChernCharacter E
• Inputs:
• Outputs:
• g, , 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 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 | | 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