Hurwitz–Belyi maps

David P. Roberts

doi:10.5802/pmb.21

Hurwitz–Belyi maps

David P. Roberts ¹

¹ Division of Science and Mathematics, University of Minnesota Morris, Morris, Minnesota, 56267, USA

Publications mathématiques de Besançon. Algèbre et théorie des nombres (2018), pp. 25-67.

Abstract
Résumé

The study of the moduli of covers of the projective line leads to the theory of Hurwitz varieties covering configuration varieties. Certain one-dimensional slices of these coverings are particularly interesting Belyi maps. We present systematic examples of such “Hurwitz–Belyi maps”. Our examples illustrate a wide variety of theoretical phenomena and computational techniques.

L’étude des modules de revêtements de la droite projective conduit à la théorie des variétés de Hurwitz comme revêtements des variétés de configurations. Certaines sections de dimension un des ces revêtements sont des applications de Belyi particulièrement intéressantes. Nous présentons des exemples de telles applications « d’Hurwitz–Belyi » qui illustrent une large variété de phénomènes théoriques et techniques de calculs.

Published online: 2018-06-20

DOI: 10.5802/pmb.21

Classification: 11G32, 14H57
Mots-clés : Hurwitz variety, Belyi map, ramification

Author's affiliations:

David P. Roberts ¹

¹ Division of Science and Mathematics, University of Minnesota Morris, Morris, Minnesota, 56267, USA

License:

CC-BY-ND 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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David P. Roberts. Hurwitz–Belyi maps. Publications mathématiques de Besançon. Algèbre et théorie des nombres (2018), pp. 25-67. doi : 10.5802/pmb.21. https://pmb.centre-mersenne.org/articles/10.5802/pmb.21/

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