A Hurwitz surface is a specific type of mathematical object in the field of algebraic geometry and topology. It is a smooth (or complex) surface that arises in the study of branched covers of Riemann surfaces. More specifically, Hurwitz surfaces are associated with the study of coverings of the Riemann sphere (the complex projective line) and are tied to the Hurwitz problem, which deals with the enumeration of branched covers of a surface.
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