Meromorphic function as a holomorphic map to the Riemann sphere
ID: meromorphic-function-as-a-holomorphic-map-to-the-riemann-sphere
A meromorphic function on a Riemann surface is equivalently a holomorphic map to the Riemann sphere, with every pole mapped to infinity. Composition with a rational self-map of the sphere is again such a holomorphic map.
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