Arithmeticity of the monodromy of the Wiman-Edge pencil

2019/11/04 by Farb, Benson, Looijenga, Eduard · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1911.01210

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 \Af₅. 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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