Arithmeticity of the monodromy of the Wiman-Edge pencil

Benson Farb; Eduard Looijenga

doi:10.5802/aif.3423

Arithmeticity of the monodromy of the Wiman-Edge pencil

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

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.

Original language	English
Pages (from-to)	1325-1361
Number of pages	36
Journal	Annales de l'Institut Fourier
Volume	71
Issue number	4
DOIs	https://doi.org/10.5802/aif.3423
Publication status	Published - 8 Dec 2021

Keywords

Mathematics - Algebraic Geometry
Mathematics - Geometric Topology

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10.5802/aif.3423Licence: CC BY-ND

AIF_2021__71_4_1325_0 (1)Final published version, 3.4 MBLicence: CC BY-ND

http://adsabs.harvard.edu/abs/2019arXiv191101210F

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abstract = "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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AU - Looijenga, Eduard

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AB - 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.

KW - Mathematics - Algebraic Geometry

KW - Mathematics - Geometric Topology

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DO - 10.5802/aif.3423

M3 - Article

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JO - Annales de l'Institut Fourier

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Arithmeticity of the monodromy of the Wiman-Edge pencil

Abstract

Keywords

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