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Composite genus one Belyi maps

Vidunas, R. and He, Y. ORCID: 0000-0002-0787-8380 (2018). Composite genus one Belyi maps. Indagationes Mathematicae, 29(3), pp. 916-947. doi: 10.1016/j.indag.2018.02.001

Abstract

Motivated by a demand for explicit genus 1 Belyi maps from theoretical physics, we give an efficient method of explicitly computing genus one Belyi maps by (1) composing covering maps from elliptic curves to the Riemann sphere with simpler (univariate) genus zero Belyi maps, as well as by (2) composing further with isogenies between elliptic curves. The computed examples of genus 1 Belyi maps has doubly-periodic dessins d’enfant that are listed in the physics literature as so-called brane-tilings in the context of quiver gauge theories

Publication Type: Article
Additional Information: © 2018 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords: Dessin d’enfants, Belyi covering, Bipartite graphs, Gauge theories, Elliptic curves, Isogenies
Subjects: Q Science > QA Mathematics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: http://openaccess.city.ac.uk/id/eprint/20365
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