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ampleKClass -- the class of an ample line bundle

Synopsis

Description

If $X$ is a GKM variety with a distinguished ample equivariant line bundle, this method returns the KClass of the line bundle. If no such line bundle is defined, it allows the user to construct one.

The following example describes the ample line bundle on the Lagrangian Grassmannian $SpGr(2,4)$. The line bundle is precisely the pullback of O(1) under the Plücker embedding $SpGr(2,4) \to \mathbb P^4$.

i1 : SpGr24 = generalizedFlagVariety("C",2,{2})

o1 = a "GKM variety" with an action of a 2-dimensional torus

o1 : GKMVariety
 
i2 : O1 = ampleKClass SpGr24

o2 = an "equivariant K-class" on a GKM variety 

o2 : KClass
 
i3 : peek O1

o3 = KClass{variety => a "GKM variety" with an action of a 2-dimensional torus}
                                                          -1
            KPolynomials => HashTable{{set {0, 1*}} => T T    }
                                                        0 1
                                      {set {0, 1}} => T T
                                                       0 1
                                                         -1 -1
                                      {set {1*, 0*}} => T  T
                                                         0  1
                                                        -1
                                      {set {1, 0*}} => T  T
                                                        0  1

See also

Ways to use ampleKClass :

For the programmer

The object ampleKClass is a method function.