The Cartesian product of varieties X0, X1, X2, …, all defined over the same ground field k, is the fiber product X0 ×k X1 ×k X2 ×k …. For normal toric varieties, the fan of the product is given by the Cartesian product of the underlying fans of the factors.
i1 : X = toricProjectiveSpace 1; |
i2 : Y = toricProjectiveSpace 2; |
i3 : Z = toricProjectiveSpace 3; |
i4 : Seq = (X, Y, Z); |
i5 : P = cartesianProduct Seq; |
i6 : dim P o6 = 6 |
i7 : assert (dim P == 1+2+3) |
i8 : factors = components P o8 = {X, Y, Z} o8 : List |
i9 : # factors o9 = 3 |
i10 : assert (factors#0 === X and factors#1 === Y and factors#2 === Z) |
This general method for constructing products is invoked by all of the other product constructors.