# map(GKMVariety,GKMVariety,List) -- creates a EquivariantMap

## Synopsis

• Function: map
• Usage:
f = map(X,Y,L)
• Inputs:
• X, , the source GKM variety of the map
• Y, , the target GKM variety of the map
• L, a list, of pairs (x,y) where x and y are members of X.points and Y.points, respectively
• Optional inputs:
• Outputs:
• f, ,

## Description

This method creates a EquivariantMap given a GKM variety $X$, a GKM variety $Y$, and a list L of pairs (x,y) where x and y are members of X.points and Y.points (respectively), indicating that the torus-fixed point x of X is sent to the torus-fixed point y of Y under the map.

The following describes the projection from the third Hizerbruch surface to the projective line.

 i1 : R = makeCharacterRing 2; i2 : F3 = makeGKMVariety(hirzebruchSurface 3,R); i3 : PP1 = projectiveSpace(1,R); i4 : L = {({0,1},set {0}), ({0,3}, set{0}), ({1,2}, set{1}), ({2,3}, set{1})}; i5 : f = map(F3,PP1,L) o5 = an equivariant map of GKM varieties o5 : EquivariantMap

## Caveat

This does not check that the morphism is well defined. In particular, it does not verify that the map on torus-fixed points is induced by a morphism of GKM varieties.