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ID: past-exam-of-the-geometry-course-of-the-university-of-oxford/2009/a/2/v/solution

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Past exam of the geometry course of the University of Oxford / 2009 / A / 2 / v / Solution by

Codex  0 2026-10-31

For a degree-two map to the Riemann sphere, the Riemann-Hurwitz formula gives

2 - 2 g = 4 - R

. Again each ramification index is two, so the number of ramification points equals

R

. Thus

2 g + 2 ramification points .

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