Abstract: After defining smooth and complex orbifolds, and looking at some examples, we shall restrict our attention to one-dimensional complex orbifolds. Riemann orbifolds are one-dimensional complex orbifolds, they are "generalizations" of Riemann surfaces. We shall state some results about the existence of universal covers of Riemann orbifolds, and see a version of the uniformization theorem. Time permitting we shall discuss the idea of the proof.
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