makeKClass -- constructs an equivariant K-class

Synopsis

Usage:

C = makeKClass(X,L)
Inputs:
- X, a GKM variety,
- L, a list, of Laurent polynomials corresponding to each torus-fixed point
- D, a toric divisor,
Outputs:
- C, an equivariant K-class,

Description

This method creates a KClass given a GKMVariety X and a list L of Laurent polynomials in its character ring. The order of Laurent polynomials in the list must correspond to the order of the list of torus-fixed points X.points.

The following example is the class of $O(1)$ on the projective space $\mathbb P^3$.

i1 : PP3 = projectiveSpace 3;

i2 : R = PP3.characterRing;

i3 : L = gens R

o3 = {T , T , T , T }
       0   1   2   3

o3 : List

i4 : C = makeKClass(PP3,L) --the class of O(1) on PP3

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

o4 : KClass

i5 : C === ampleKClass PP3

o5 = true

i6 : isWellDefined C

o6 = true

Caveat

This function does not check if X defines a GKM variety - see isWellDefined.

Ways to use makeKClass :

makeKClass(GKMVariety,List)
makeKClass(GKMVariety,FlagMatroid) -- the equivariant K-class of a flag matroid
makeKClass(GKMVariety,ToricDivisor) -- create the KClass from a ToricDivisor

For the programmer

The object makeKClass is a method function.