# ampleKClass -- the class of an ample line bundle

## Synopsis

• Usage:
ampleKClass(X)
• Inputs:
• X, ,
• C, ,
• Outputs:

## 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 -1 KPolynomials => HashTable{{set {0*, 1*}} => T T } 0 1 -1 {set {0*, 1}} => T T 0 1 -1 {set {0, 1*}} => T T 0 1 {set {0, 1}} => T T 0 1