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NormalToricVarieties :: dim(NormalToricVariety)

dim(NormalToricVariety) -- get the dimension of a normal toric variety

Synopsis

Description

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 d 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 = 5
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

See also