In this talk, I would like to give an analytic construction of the Hurwitz space showing that it is a complex manifold. As an application, we will give a short prooof of irreducibility of moduli space of smooth projective curves. 

 

Reference:

William Fulton, Hurwitz Schemes and Irreducibility of Moduli of Algebraic Curves, Annals of Mathematics, Second Series, Vol. 90, No. 3 (Nov., 1969), pp. 542-575.

 

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