Negation is a biholomorphic involution of . Its fixed points satisfy , so they are indexed by the four elements of .
Away from the four fixed points, negation acts freely and the quotient map is a holomorphic double covering. Near a fixed point, an invariant coordinate is , so the quotient extends across the image as a Riemann surface and the map has ramification index two. The Riemann-Hurwitz formula giveshence the quotient has genus zero and is biholomorphic to the Riemann sphere.
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