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Ramification (mathematics)

Ramification

{title2=$R_f$}

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 $2g_X-2=(\deg f)(2g_Y-2)+\deg R_f$.

The coefficients assemble the <ramification indices of a morphism of curves>.

Ramification divisor

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Ramification divisor ( $R_{f}$ )

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Ramification divisor (Rf​)

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