Year: 2010
Type: preprint
Abstract: In this work, we determine all Lattes maps which are Belyi morphisms. It turns out that in the generic case, i.e. when the automorphism group is $\ZZ/2\ZZ$, the corresponding family of Lattes maps are Belyi morphisms if and only if the isogeny is multiplication by two. This family form a continuous family of Belyi maps. Elliptic curves with complex multiplication also determine a family over $\ZZ$ of Belyi morphisms. We give the explicit formulas for the first few Belyi morphisms when the curve has complex multiplication by 3rd root of unity.
Source: arXiv (Cornell University)
Author: Zeytin, Ayberk
Institution: Galatasaray University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4302282508