 Canonical class of the rational elliptic surface

ID: canonical-class-of-the-rational-elliptic-surface

H

for the pullback of a line and

E_{1}, \dots, E_{9}

for the exceptional classes, a fiber has class

F = 3 H - \sum_{i} E_{i}

, while the blowup formula gives

K_{E (1)} = - 3 H + \sum_{i} E_{i} = - F .

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