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GKMVarieties :: makeKClass(GKMVariety,ToricDivisor)

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

Synopsis

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.

See also