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NormalToricVarieties :: max(NormalToricVariety)

max(NormalToricVariety) -- get the maximal cones in the associated fan

Synopsis

Description

A normal toric variety corresponds to a strongly convex rational polyhedral fan in affine space. 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. The fan is encoded by the minimal nonzero lattice points on its rays and the set of rays defining the maximal cones (i.e. a maximal cone is not properly contained in another cone in the fan). The rays are ordered and indexed by nonnegative integers: 0,…, n. Using this indexing, a maximal cone in the fan corresponds to a sublist of {0,…,n}; the entries index the rays that generate the cone.

The examples show the maximal cones for the projective plane, projective 3-space, a Hirzebruch surface, and a weighted projective space.

PP2 = projectiveSpace 2;
#rays PP2
max PP2
PP3 = projectiveSpace 3;
#rays PP3
max PP3
FF7 = hirzebruchSurface 7;
#rays FF7
max FF7
X = weightedProjectiveSpace {1,2,3};
#rays X
max X
A list corresponding to the maximal cones in the fan is part of the defining data of a toric variety.

See also