Hirzebruch surface
= Hirzebruch surface
{c}
{title2=$\mathbb F_k$}
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The Hirzebruch surface is the ruled surface
$$
\mathbb F_k=\mathbb P_{\mathbb P^1}(\mathcal O\oplus\mathcal O(k)).
$$
It is the smooth toric surface with rays $(1,0),(0,1),(-1,k),(0,-1)$.