# toricChernCharacter -- computes the toric Chern character of a toric vector bundle

## Synopsis

• Usage:
c = toricChernCharacter E
• Inputs:
• Outputs:
• c, , whose keys are maximal cones and the value of a key is a list of one column matrices
• Consequences:
• The result of toricChernCharacter will be stored as a cacheValue in E.cache#toricChernCharacter. It will be used by other methods.

## Description

Given a toric vector bundle in Klyachko's description, toricChernCharacter computes its toric Chern character as introduced in [P].
toricChernCharacter calles internally the method compatibleBases.
 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 : 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