Computation of highly ramified coverings

Vidūnas, Raimundas; Kitaev, Alexander

doi:10.1090/S0025-5718-09-02233-9

Computation of highly ramified coverings

Authors: Raimundas Vidunas and Alexander V. Kitaev
Journal: Math. Comp. 78 (2009), 2371-2395
MSC (2000): Primary 57M12, 34M55; Secondary 33E17
DOI: https://doi.org/10.1090/S0025-5718-09-02233-9
Published electronically: February 11, 2009
MathSciNet review: 2521293
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Abstract: An almost Belyi covering is an algebraic covering of the projective line, such that all ramified points except one simple ramified point lie above a set of 3 points of the projective line. In general, there are 1-dimensional families of these coverings with a fixed ramification pattern. (That is, Hurwitz spaces for these coverings are curves.) In this paper, three almost Belyi coverings of degrees 11, 12, and 20 are explicitly constructed. We demonstrate how these coverings can be used for computation of several algebraic solutions of the sixth Painlevé equation.

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