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GKMVarieties : Table of Contents
GKMVarieties
-- computations with GKM varieties and moment graphs
affineToricRing
-- computes the toric ring associated to a monomial map
ampleKClass
-- the class of an ample line bundle
bases(FlagMatroid)
-- compute the bases of a flag matroid
bruhatOrder
-- computes the Bruhat order on a generalized flag variety
cellOrder
-- the poset of a stratification of a GKM variety
cellOrder(MomentGraph,Poset)
-- define a cell order on a moment graph
charts
-- outputs the torus-invariant affine charts of a GKM variety
compose(EquivariantMap,EquivariantMap)
-- computes the composition of two equivariant morphisms
diagonalMap
-- constructs the diagonal morphism
EquivariantMap
-- the class of all equivariant morphisms between GKM varieties
EquivariantMap ** EquivariantMap
-- computes the product of two equivariant morphisms
euler(KClass)
-- computes the equivariant Euler characteristic of an equivariant K-class
Example: generalized flag varieties
Example: smooth toric varieties
flagGeomTuttePolynomial
-- computes the flag-geometric Tutte polynomial of flag matroids
flagMap
-- creates equivariant maps between generalized flag varieties
FlagMatroid
-- the class of all flag matroids
flagMatroid
-- construct a flag matroid
generalizedFlagVariety
-- makes a generalized flag variety as a GKM variety
generalizedSchubertVariety
-- create a generalized Schubert variety
GKMVariety
-- the class of all GKM varieties
GKMVariety ** GKMVariety
-- product of GKM varieties
isWellDefined(FlagMatroid)
-- check if a flag matroid is well-defined
isWellDefined(KClass)
-- whether the input is a well-defined equivariant K-class
KClass
-- the class of all equivariant K-classes
KClass * KClass
-- computes the product of two equivariant K-classes
KClass + KClass
-- computes the sum of two equivariant K-classes
KClass ^ ZZ
-- computes powers of an equivariant K-classes
latticePoints(FlagMatroid)
-- lattice points of a base polytope of a flag matroid
lieType
-- outputs the Lie type of a generalized flag variety
makeCharacterRing
-- constructs the character ring of a torus
makeGKMVariety
-- constructs a GKM variety
makeKClass
-- constructs an equivariant K-class
makeKClass(GKMVariety,FlagMatroid)
-- the equivariant K-class of a flag matroid
makeKClass(GKMVariety,ToricDivisor)
-- create the KClass from a ToricDivisor
map(GKMVariety,GKMVariety,List)
-- creates a EquivariantMap
MomentGraph
-- the class of all moment graphs
momentGraph
-- creates a moment graph
MomentGraph ** MomentGraph
-- the product of two moment graphs
momentGraph(GKMVariety)
-- view the moment graph of a GKM variety
momentGraph(GKMVariety,MomentGraph)
-- define a moment graph for a GKM variety
normalToricVariety(GKMVariety)
-- converts a GKM variety back into a toric variety
orbitClosure
-- computes the equivariant K-class of a torus orbit closure of a point in a generalized flag variety
projectiveSpace
-- constructs projective space as a GKM variety
pullback(EquivariantMap)
-- computes the pullback map of equivariant K-classes of an equivariant map
pushforward
-- computes the pushforward map of equivariant K-classes of an equivariant map
setIndicator
-- computes the signed indicator vector of an admissible set
trivialKClass
-- the equivariant K-class of the structure sheaf
underlyingGraph(MomentGraph)
-- the underlying (undirected) graph of a moment graph