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

Solution

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

 Solution (source code)