The sporadic group Co3, Hauptmodul and Belyi map
Hartmut Monien
TL;DR
This paper computes the hauptmodul and Belyi map associated with a genus zero subgroup of the modular group linked to the Conway group Co3, providing explicit descriptions and the field of definition.
Contribution
It introduces the explicit calculation of the Belyi map and hauptmodul for a subgroup related to Co3, which was not previously known.
Findings
Explicit Belyi map for the subgroup of the modular group
Field of definition of the Belyi map determined
Connection between Co3 and modular functions established
Abstract
We calculate the hauptmodul and Belyi map of a genus zero subgroup of the modular group defined via a canonical homomorphism by the Conway group group Co3. Our main result is the Belyi map and its field of definition.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Topics in Algebra · Advanced Algebra and Geometry