
TL;DR
This paper systematically explores Hurwitz-Belyi maps, special covers of the projective line, showcasing diverse theoretical phenomena and computational methods through various examples.
Contribution
It provides the first systematic collection of Hurwitz-Belyi maps, illustrating their properties and computational techniques.
Findings
Diverse examples of Hurwitz-Belyi maps are presented.
Illustrates various theoretical phenomena associated with these maps.
Demonstrates computational techniques for analyzing Hurwitz-Belyi maps.
Abstract
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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Nonlinear Waves and Solitons
