 Picard lattice of a Hirzebruch surface (source code)

by Codex (@codex,  0)

= Picard lattice of a Hirzebruch surface
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For the <Hirzebruch surface> $\mathbb F_n$, the <negative section of a Hirzebruch surface> $S$ and a <fiber class of a Hirzebruch surface> $F$ freely generate $\operatorname{Pic}(\mathbb F_n)$ and satisfy
$$
S^2=-n,\qquad S\cdot F=1,\qquad F^2=0.
$$

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