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GKMVarieties :: diagonalMap

diagonalMap -- constructs the diagonal morphism

Synopsis

Description

Given a GKM variety $X$ this method constructs a EquivariantMap representing the diagonal morphism $X \to X \times X$. Note that $X \times X$ is a GKM variety via the diagonal action of the torus.

i1 : X = generalizedFlagVariety("A",3,{2}); -- The Grassmannian Gr(2,4)
i2 : f = diagonalMap X;
i3 : peek f

o3 = EquivariantMap{cache => CacheTable{}                                            }
                    ptsMap => HashTable{{set {0, 1}} => ({set {0, 1}}, {set {0, 1}})}
                                        {set {0, 2}} => ({set {0, 2}}, {set {0, 2}})
                                        {set {0, 3}} => ({set {0, 3}}, {set {0, 3}})
                                        {set {1, 2}} => ({set {1, 2}}, {set {1, 2}})
                                        {set {1, 3}} => ({set {1, 3}}, {set {1, 3}})
                                        {set {2, 3}} => ({set {2, 3}}, {set {2, 3}})
                    source => a GKM variety with an action of a 4-dimensional torus
                    target => a GKM variety with an action of a 4-dimensional torus

See also

Ways to use diagonalMap :

For the programmer

The object diagonalMap is a method function.