The {em Wiman-Edge pencil} is the universal family $Cs/mathcal B$ of projective, genus $6$, complex-algebraic curves admitting a faithful action of the icosahedral group $Af_5$. The goal of this paper is to prove that the monodromy of $Cs/mathcal B$ is commensurable with a Hilbert modular group; in particular is arithmetic. We then give a modular interpretation of this, as well as a uniformization of $mathcal B$.
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