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'') |