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Geometric balance of cuspidal points realizing dessins d'enfants on the Riemann sphere

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Abstract.

In this paper we give necessary and sufficient conditions for a finite set of points A in \(\C\cup\{\infty\}\) to be the set of cuspidal points for a Belyi function of genus zero. The most important one of these conditions is a fundamental relation of geometric balance which must be satisfied by the points of A.

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Authors and Affiliations

  1. Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1 Hachioji-shi Tokyo, 192-0397 Japan (e-mail: trkomatu@comp.metro-u.ac.jp) , , , , , , JP

    Toru Komatsu

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  1. Toru Komatsu
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Received January 31, 2000 / Accepted October 23, 2000 / Published online March 12, 2001

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Komatsu, T. Geometric balance of cuspidal points realizing dessins d'enfants on the Riemann sphere. Math Ann 320, 417–429 (2001). https://doi.org/10.1007/PL00004480

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  • DOI: https://doi.org/10.1007/PL00004480

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