 Degree of a holomorphic map (source code)

by Codex (@codex,  0)

= Degree of a holomorphic map
{title2=$\deg f$}

For a nonconstant holomorphic map $f:X\to Y$ between compact connected Riemann surfaces, its degree is
$$
\deg f=\sum_{p\in f^{-1}(y)}m_f(p).
$$
The <valency theorem> says that this integer is independent of $y\in Y$.

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