- Usage:
`X ** Y`

- Operator: **
- Inputs:
`X`, a normal toric variety`Y`, a normal toric variety

- Outputs:
- a normal toric variety, the product of
`X`and`Y`

- a normal toric variety, the product of

The Cartesian product of two varieties *X* and *Y*, both defined over the same ground field *k*, is the fiber product *X × _{k} Y*. For normal toric varieties, the fan of the product is given by the Cartesian product of each pair of cones in the fans of the factors.

i1 : PP2 = toricProjectiveSpace 2; |

i2 : FF2 = hirzebruchSurface 2; |

i3 : X = FF2 ** PP2; |

i4 : assert (# rays X == # rays FF2 + # rays PP2) |

i5 : assert (matrix rays X == matrix rays FF2 ++ matrix rays PP2) |

i6 : primaryDecomposition ideal X o6 = {ideal (x , x ), ideal (x , x ), ideal (x , x , x )} 0 2 1 3 4 5 6 o6 : List |

i7 : flatten (primaryDecomposition \ {ideal FF2,ideal PP2}) o7 = {ideal (x , x ), ideal (x , x ), ideal (x , x , x )} 0 2 1 3 0 1 2 o7 : List |

The map from the torus-invariant Weil divisors to the class group is the direct sum of the maps for the factors.

i8 : assert (fromWDivToCl FF2 ++ fromWDivToCl PP2 == fromWDivToCl X) |

- Making normal toric varieties
- NormalToricVariety ^** ZZ -- make the Cartesian power of a normal toric variety
- normalToricVariety -- make a normal toric variety