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GKMVarieties :: projectiveSpace

projectiveSpace -- constructs projective space as a GKM variety

Synopsis

Description

Given an integer $n$ this method constructs the n-dimensional projective space, $\mathbb P^n$, as a GKM variety. The action of $(\mathbb C^*)^{n+1}$ on $\mathbb P^n$ is defined by $(t_0, \ldots, t_n) \cdot (x_0, \ldots, x_n) = (t_0^{-1}x_0, \ldots, t_n^{-1}x_n)$.

i1 : PP4 = projectiveSpace 4;
i2 : peek PP4

o2 = GKMVariety{cache => CacheTable{...1...}                                                                            }
                characterRing => ZZ[T ..T ]
                                     0   4
                charts => HashTable{set {0} => {{-1, 1, 0, 0, 0}, {-1, 0, 1, 0, 0}, {-1, 0, 0, 1, 0}, {-1, 0, 0, 0, 1}}}
                                    set {1} => {{1, -1, 0, 0, 0}, {0, -1, 1, 0, 0}, {0, -1, 0, 1, 0}, {0, -1, 0, 0, 1}}
                                    set {2} => {{1, 0, -1, 0, 0}, {0, 1, -1, 0, 0}, {0, 0, -1, 1, 0}, {0, 0, -1, 0, 1}}
                                    set {3} => {{1, 0, 0, -1, 0}, {0, 1, 0, -1, 0}, {0, 0, 1, -1, 0}, {0, 0, 0, -1, 1}}
                                    set {4} => {{1, 0, 0, 0, -1}, {0, 1, 0, 0, -1}, {0, 0, 1, 0, -1}, {0, 0, 0, 1, -1}}
                momentGraph => a moment graph on 5 vertices with 10 edges 
                points => {set {0}, set {1}, set {2}, set {3}, set {4}}

See also

Ways to use projectiveSpace :

For the programmer

The object projectiveSpace is a method function.