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Computation of Belyi maps with prescribed ramification and applications in Galois theory. (English) Zbl 07286497
Summary: We compute genus-0 Belyi maps with prescribed monodromy groups and verify the computed results. Among the computed examples are almost simple primitive groups that satisfy the well known rational rigidity criterion yielding polynomials with prescribed Galois groups over \(\mathbb{Q}(t)\). We also give an explicit version of a theorem of Magaard, which predicts all sporadic groups occurring as composition factors of monodromy groups of rational functions.
MSC:
14 Algebraic geometry
12 Field theory and polynomials
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