There is no special code of products of projective spaces, but you can 
easily construct them as products of toric varieties:

sage: fan1 = toric_varieties.P1()
sage: fan1 = toric_varieties.P1().fan()
sage: fan2 = toric_varieties.P2().fan()
sage: P1xP2 = ToricVariety(fan1.cartesian_product(fan2))


On Tuesday, November 6, 2012 9:57:37 AM UTC-5, Ben wrote:
>
> Is there currently a way to define a product of projective spaces. (i.e. 
> $\mathbb{P}^n \times \mathbb{P}^m$), then be able to work with projections 
> to either component, points, subschemes, etc.
>
> Thanks,
>   Ben
>

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