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NormalToricVarieties :: NormalToricVariety ^** ZZ

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

Synopsis

Description

The i-ary Cartesian product of the variety X, defined over the ground field k, is the i-ary fiber product of X with itself over k. For a normal toric variety, the fan of the i-ary Cartesian product is given by the i-ary Cartesian product of the cones.

i1 : PP2 = toricProjectiveSpace 2;
i2 : X = PP2 ^** 4;
i3 : fromWDivToCl X

o3 = | 1 1 1 0 0 0 0 0 0 0 0 0 |
     | 0 0 0 1 1 1 0 0 0 0 0 0 |
     | 0 0 0 0 0 0 1 1 1 0 0 0 |
     | 0 0 0 0 0 0 0 0 0 1 1 1 |

              4        12
o3 : Matrix ZZ  <--- ZZ
i4 : FF2 = hirzebruchSurface (2);
i5 : Y = FF2 ^** 3;
i6 : fromWDivToCl Y

o6 = | 1 -2 1 0 0 0  0 0 0 0  0 0 |
     | 0 1  0 1 0 0  0 0 0 0  0 0 |
     | 0 0  0 0 1 -2 1 0 0 0  0 0 |
     | 0 0  0 0 0 1  0 1 0 0  0 0 |
     | 0 0  0 0 0 0  0 0 1 -2 1 0 |
     | 0 0  0 0 0 0  0 0 0 1  0 1 |

              6        12
o6 : Matrix ZZ  <--- ZZ
i7 : X' = PP2 ** PP2;
i8 : X'' = PP2 ^** 2;
i9 : assert (rays X' == rays X'' and  max X' == max X'')

See also