Description
Given a toric vector bundle
E in Klyachko’s description on a toric variety
X = TV(Σ), it is encoded by increasing filtrations
Eρ(j) for each ray
ρ∈Σ(1). To these filtrations we can associated the set
L(E) of intersections
∩ρ Eρ (jρ), where
(jρ)ρ runs over all tuples in
ℤΣ(1). This set
L(E) is ordered by inclusion and there is a unique matriod
M(E) associated to it, see [RJS, Proposition 3.1].
groundSet computes the ground set (i.e. building blocks) of this matroid.
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 : groundSet E
o2 = {| 1 |, | 1 |, | 0 |}
| 1 | | 0 | | 1 |
o2 : List
|
With the ground set, one can compute the parliament of polytopes using
parliament or compute the set of compatible bases using
compatibleBases.