Minimal Hirzebruch surface
= Minimal Hirzebruch surface
{c}
The <Hirzebruch surface> $\mathbb F_n$ is minimal for $n=0$ and every $n\geq2$; $\mathbb F_1$ is not minimal because its negative section is a $(-1)$-curve. For $n>0$, the negative section is the unique irreducible curve of negative self-intersection, so its self-intersection $-n$ distinguishes the isomorphism class. The surfaces $\mathbb F_n$ for $n\geq2$ therefore give infinitely many pairwise nonisomorphic minimal rational surfaces.