Hurwitz space

Moduli spaces of ramified covers

In mathematics, in particular algebraic geometry, Hurwitz spaces are moduli spaces of ramified covers of the projective line, and they are related to the moduli of curves. Their rational points are of interest for the study of the inverse Galois problem, and as such they have been extensively studied by arithmetic geometers. More precisely, Hurwitz spaces classify isomorphism classes of Galois covers with a given automorphism group and a specified number of branch points. The monodromy conjugacy classes at each branch point are also commonly fixed. These spaces have been introduced by Adolf Hurwitz which showed the connectedness of the Hurwitz spaces in the case of simply branched covers.

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