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 |
The factors are cached and can be accessed with components.
i4 : factors = components X o4 = {PP2, PP2, PP2, PP2} o4 : List |
i5 : assert (# factors === 4) |
i6 : assert all (4, i -> factors#i === PP2) |
i7 : FF2 = hirzebruchSurface (2); |
i8 : Y = FF2 ^** 3; |
i9 : fromWDivToCl Y o9 = | 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 o9 : Matrix ZZ <--- ZZ |
i10 : X' = PP2 ** PP2; |
i11 : X'' = PP2 ^** 2; |
i12 : assert (rays X' == rays X'' and max X' == max X'') |