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

Synopsis

Function: map
Usage:

f = map(X,Y,L)
Inputs:
- X, a GKM variety, the source GKM variety of the map
- Y, a GKM variety, 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:
- Degree => ..., default value null,
- DegreeLift => ..., default value null,
- DegreeMap => ..., default value null,
Outputs:
- f, an equivariant map,

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.

Ways to use this method: