Quotient of a one-dimensional complex torus by negation
= Quotient of a one-dimensional complex torus by negation
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 $w=z^2$, so the quotient extends across the image as a Riemann surface and the map has ramification index two. The <Riemann-Hurwitz formula> gives
$$
0=2(2g-2)+4,
$$
hence the quotient has genus zero and is biholomorphic to the <Riemann sphere>.