- Usage:
`max X`

- Function: max
- Inputs:
`X`, a normal toric variety

- Outputs:
- a list, of lists of nonnegative integers; each entry indexes the rays that generate a maximal cone in the fan

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 *ℚ ^{d}* with underlying lattice

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

i1 : PP1 = toricProjectiveSpace 1; |

i2 : # rays PP1 o2 = 2 |

i3 : max PP1 o3 = {{0}, {1}} o3 : List |

i4 : PP3 = toricProjectiveSpace 3; |

i5 : # rays PP3 o5 = 4 |

i6 : max PP3 o6 = {{0, 1, 2}, {0, 1, 3}, {0, 2, 3}, {1, 2, 3}} o6 : List |

i7 : FF7 = hirzebruchSurface 7; |

i8 : # rays FF7 o8 = 4 |

i9 : max FF7 o9 = {{0, 1}, {0, 3}, {1, 2}, {2, 3}} o9 : List |

i10 : X = weightedProjectiveSpace {1,2,3}; |

i11 : # rays X o11 = 3 |

i12 : max X o12 = {{0, 1}, {0, 2}, {1, 2}} o12 : List |

In this package, a list corresponding to the maximal cones in the fan is part of the defining data of a normal toric variety.

- Making normal toric varieties
- Basic invariants and properties of normal toric varieties
- rays(NormalToricVariety) -- get the rays of the associated fan