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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 $\QQ^d$ with underlying lattice $N = \ZZ^d$. 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 = X

o6 : NormalToricVariety
i7 : dim X

o7 = 3
i8 : isDegenerate X

o8 = true

In this package, number of entries in any ray equals the dimension of both the underlying lattice and the normal toric variety, so this method does essentially no computation.

See also