The dimension of a normal toric variety equals the dimension of its dense algebraic torus. In this package, the fan associated to a normal
d-dimensional toric variety lies in the rational vector space
ℚd with underlying lattice
N = ℤd. Hence, the dimension equals the number of entries in a minimal nonzero lattice point on a ray.
The following examples illustrate normal toric varieties of various dimensions.
i1 : dim projectiveSpace 1
o1 = 1
|
i2 : dim projectiveSpace 5
o2 = 5
|
i3 : dim hirzebruchSurface 7
o3 = 2
|
i4 : dim weightedProjectiveSpace {1,2,2,3,4}
o4 = 4
|
i5 : W = normalToricVariety({{4,-1,0},{0,1,0}},{{0,1}})
o5 = W
o5 : NormalToricVariety
|
i6 : dim W
o6 = 3
|
i7 : isDegenerate W
o7 = true
|