no. 4
Arithmeticity of the monodromy of the Wiman–Edge pencil
[L’arithméticité de la monodromie du pinceau de Wiman–Edge]
Farb, Benson1 ; Looijenga, Eduard2, 3
1 Dept. of Mathematics University of Chicago (USA)
2 Yau Mathematical Sciences Center Tsinghua University, Beijing (China)
3 Utrecht University (The Netherlands)
Annales de l'Institut Fourier, Tome 71 (2021) no. 4, pp. 1325-1361.

Le pinceau de Wiman–Edge est une famille universelle de courbes projectives non singulières de genre 6 et munie d’une action fidèle du groupe icosahédral. Le but principal de ce travail est la détermination de son groupe de monodromie. Nous montrons que ce groupe est arithmétique et commensurable avec un groupe modulaire de Hilbert. Nous donnons une interprétation modulaire de ce fait et décrivons en plus une uniformisation de la base.

The Wiman–Edge pencil is the universal family of projective, genus 6, complex-algebraic curves endowed with a faithful action of the icosahedral group. The goal of this paper is to prove that its monodromy group 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 its base.

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DOI : 10.5802/aif.3423
Classification : 14H45, 14H10, 14H37
Keywords: Wiman–Edge pencil, monodromy group
Mot clés : Pinceau de Wiman–Edge, groupe de monodromie
Farb, Benson 1 ; Looijenga, Eduard 2, 3

1 Dept. of Mathematics University of Chicago (USA)
2 Yau Mathematical Sciences Center Tsinghua University, Beijing (China)
3 Utrecht University (The Netherlands) 
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Farb, Benson; Looijenga, Eduard. Arithmeticity of the monodromy of the Wiman–Edge pencil. Annales de l'Institut Fourier, Tome 71 (2021) no. 4, pp. 1325-1361. doi : 10.5802/aif.3423. http://www.numdam.org/articles/10.5802/aif.3423/

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