Arithmeticity of the monodromy of the Wiman-Edge pencil

The {\em Wiman-Edge pencil} is the universal family $\text{Cs}\mathrm{/}\mathcal{B}$ of projective, genus $6$, complex-algebraic curves admitting a faithful action of the icosahedral group ${\text{Af}}_5$. The goal of this paper is to prove that the monodromy of $\text{Cs}\mathrm{/}\mathcal{B}$ 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 $\mathcal{B}$.