makeKClass(GKMVariety,ToricDivisor) -- create the KClass from a ToricDivisor

Synopsis

Function: makeKClass
Usage:

C = makeKClass(X,D)
Inputs:
- X, a GKM variety, created from a NormalToricVariety
- D, a toric divisor,
Outputs:
- C, an equivariant K-class,

Description

If a GKM variety $X$ also admits a structure of a NormalToricVariety, then the following example shows how to obtain the KClass of any ToricDivisor on $X$.

i1 : X = toricProjectiveSpace 3;

i2 : D = toricDivisor({1,0,0,0},X) -- the class of O(1) on P^3

o2 = X
      0

o2 : ToricDivisor on X

i3 : Y = makeGKMVariety X; -- The torus is C^3 not C^4

i4 : C = makeKClass(Y,D)

o4 = an "equivariant K-class" on a GKM variety 

o4 : KClass

i5 : assert(isWellDefined C)

i6 : peek C

o6 = KClass{variety => a "GKM variety" with an action of a 3-dimensional torus}
                                                    -1
            KPolynomials => HashTable{{0, 1, 2} => T  }
                                                    2
                                                    -1
                                      {0, 1, 3} => T
                                                    1
                                                    -1
                                      {0, 2, 3} => T
                                                    0
                                      {1, 2, 3} => 1

Caveat

Toric vector bundles are yet to be imported.

Ways to use this method: