 Solution

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

The ramification sum equals

2 g - 2 + 2 d

. Since

g \geq 0

and

d > 1

, it is at least

2 d - 2 > 0

. Thus some point has analytic ramification index greater than one.

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