City Research Online

Abstract

We present a method of obtaining a Belyi map on an elliptic curve from that on the Riemann sphere. This is done by writing the former as a radical of the latter, which we call a quadratic correspondence, with the radical determining the elliptic curve. With a host of examples of various degrees, we demonstrate that the correspondence is an efficient way of obtaining genus one Belyi maps. As applications, we find the Belyi maps for the dessins d'enfant which have arisen as brane-tilings in the physics community, including ones, such as the so-called suspended pinched point, which have been a standing challenge for a number of years.

Publication Type:	Article
Additional Information:	Electronic version of an article published as Vidunas, R. and He, Y. (2020). Genus one Belyi maps by quadratic correspondences. International Journal of Mathematics, 31(5), 2050034, https://doi.org/10.1142/S0129167X20500342 © World Scientific Publishing Company, http://www.worldscientific.com/worldscinet/ijm
Publisher Keywords:	Dessins d’Enfant, elliptic curves, brane tilings
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology > Mathematics
SWORD Depositor:	Symplectic Administrator

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