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Ramification divisor ( $R_{f}$ )

For a finite morphism

f : X \to Y

of smooth curves, the ramification divisor is

R_{f} = \sum_{P \in X} (e_{P} - 1) P .

The Riemann-Hurwitz formula states

2 g_{X} - 2 = (de g f) (2 g_{Y} - 2) + de g R_{f}

.

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