Fun With Toric Varieties (I)

Toric varieties are fun things…

Proposition: The blowup of \mathbb{P}^2 at two points is isomorphic to \mathbb{P}^1\times \mathbb{P}^1 blown up at one point.

Proof:

Fan representing the blowup of P^2 at two points.

Fan for the blowup of P^2 at two points.

Fan representing the blowup of P^1 x P^1 at one point.

Fan for the blowup of P^1 x P^1 at one point.

Done.

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