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GKMVarieties :: map(GKMVariety,GKMVariety,List)

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

Synopsis

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.

See also