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## Riemann Surfaces and their Genus - 2

Differential Geometry
Tsakanikas Nickos
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### Riemann Surfaces and their Genus - 2

1. Let $X$ be a compact (connected) Riemann surface of genus $g_{X} = 0$. Show that $X$ is biholomorphic to the Riemann sphere.
2. Let $X$ be a compact (connected) Riemann surface of genus $g_{X} = 1$. Show that $X$ is biholomorphic to a complex Torus.