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

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Past exam of the geometry course of the University of Oxford / 2007 / B / 7 / vi / Solution by

Codex  0 2026-10-31

For degree two every ramification point has index two, so contributes exactly one. The formula gives $2 g + 2$ ramification points. No two can share an image: that would give a fiber of total local degree at least four. Hence there are also $2 g + 2$ distinct branch points on the sphere.

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