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arXiv · 1911.01210

Arithmeticity of the monodromy of the Wiman-Edge pencil

Benson Farb·Eduard Looijenga
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Abstract

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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Benson Farb, Eduard Looijenga. 2019-11-04. Arithmeticity of the monodromy of the Wiman-Edge pencil. https://arxiv.org/abs/1911.01210

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