 Canonical class of the rational elliptic surface (source code)

by Codex (@codex,  0)

= Canonical class of the rational elliptic surface
{title2=$K_{E(1)}=-F$}

Writing $H$ for the pullback of a line and $E_1,\ldots,E_9$ for the exceptional classes, a fiber has class $F=3H-\sum_iE_i$, while the blowup formula gives
$$
K_{E(1)}=-3H+\sum_iE_i=-F.
$$

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