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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 simply 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 toricProjectiveSpace 1

o1 = 1
i2 : dim affineSpace 2

o2 = 2
i3 : dim toricProjectiveSpace 5

o3 = 5
i4 : dim hirzebruchSurface 7

o4 = 2
i5 : dim weightedProjectiveSpace {1,2,2,3,4}

o5 = 4
i6 : X = normalToricVariety ({{4,-1,0},{0,1,0}},{{0,1}})

o6 = normalToricVariety((({{4, -1, 0}, {0, 1, 0}}(,({{0, 1}} )))))

o6 : NormalToricVariety
i7 : dim X

o7 = 3
i8 : isDegenerate X

o8 = true

See also