 Solution

ID: past-exam-of-the-geometry-course-of-the-university-of-oxford/2007/b/7/i/solution

With local indices

e_{p}

, the required specialization is

2 g (C) - 2 = - 2 d + p \in C \sum (e_{p} - 1) .

Only the finitely many points of index greater than one contribute. Their images are the branch points on the target.

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