Description
Given a toric vector bundle in Klyachko's description,
restrictToInvCurves computes its restrictions to the torus invariant curves, which are isomorphich to a direct sum of line bundles $\mathbb P^1$. Recall that on $\mathbb P^1$ any vector bundle splits into $\oplus_i O_{\mathbb P^1}(a_i)$. Therefore
restrictToInvCurves returns a hash table with keys the invariant curves and as values lists with the integers $a_i$.
By [HMP, Theorem 2.1], if all these integers$a_i$ are nonnegative or positive, the original toric vector bundle is nef or ample. Hence, the methods
isNef and
isAmple check exactly that.
restrictToInvCurves calls internally the method
toricChernCharacter; whereas
isNef and
isAmple are simple checks on the output of
restrictToInvCurves.
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 : restrictToInvCurves E
o2 = HashTable{ 1  => {2, 1}}
 1 
 0  => {2, 1}
 1 
 1  => {1, 2}
 0 
o2 : HashTable

i3 : isNef E
o3 = true

i4 : isAmple E
o4 = true

In this example we see that the vector bundle is ample, as all integers are positive.