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Imagine you have a finite proper morphism between smooth projective complex curves, say $f: X \to Y$. Denote by $S$ the image of ramification points and by $d$ the degree of $f$. Then $f_\ast \mathbb{C}$ is a local system on $Y \setminus S$. How can one calculate the monodromy $\rho: \pi(Y \setminus S) \to S_d$ and how is it related to the singularities of the connection corresponding to the local system?

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