X ** Y
The Cartesian product of two varieties $X$ and $Y$, both defined over the same ground field $k$, is the fiber product $X \times_k Y$. 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.
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The map from the torus-invariant Weil divisors to the class group is the direct sum of the maps for the factors.
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The factors are cached and can be accessed with components.
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