# makeKClass -- constructs an equivariant K-class

## Synopsis

• Usage:
C = makeKClass(X,L)
• Inputs:
• X, ,
• L, a list, of Laurent polynomials corresponding to each torus-fixed point
• D, ,
• Outputs:
• C, ,

## 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.