Geodesic
Belyi pairs corresponding to dessins d'enfants of genus $3$
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2012), pp. 62-64 
E. M. Epifanov. Belyi pairs corresponding to dessins d'enfants of genus $3$. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2012), pp. 62-64. http://geodesic.mathdoc.fr/item/VMUMM_2012_3_a13/
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     author = {E. M. Epifanov},
     title = {Belyi pairs corresponding to dessins d'enfants of genus~$3$},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2012_3_a13/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this article we discuss a question arising in the dessins d'enfants theory: we are interested in finding the defining equations for the Belyi pair of a given dessin. Low genus ($g\le2$) cases are well-studied, there exist many examples of Belyi pairs of those genera and some effective methods have been developed. We present a method which allows to find Belyi pairs of self-dual genus $3$ dessins.

[1] Belyi G.V., “O rasshireniyakh Galua maksimalnogo krugovogo polya”, Izv. AN SSSR. Ser. matem., 43:2 (1979), 267–276 | MR

[2] Zvonkin A.K., Lando S.K., Grafy na poverkhnostyakh i ikh prilozheniya, MTsNMO, M., 2010

[3] Adrianov N.M., Amburg N.Ya., Dremov V.A., Kochetkov Yu.Yu., Kreines E.M., Levitskaya Yu.A., Nasretdinova V.F., Shabat G.B., “Katalog funktsii Belogo detskikh risunkov s ne bolee chem chetyrmya rebrami”, Fund. i prikl. matem., 13:6 (2007), 35–112

[4] Bychkov B.S., Dremov V.A., Epifanov E.M., “Vychisleniya par Belogo 6-rebernykh risunkov roda 3 s netrivialnymi gruppami avtomorfizmov”, Fund. i prikl. matem., 13:6 (2007), 137–148

[5] Shabat G.B., Voevodsky V.A., “Drawing curves over number fields”, The Grothendieck Festschrift, 3, Birkhäuser, Boston, 1990, 199–227 | DOI | MR

[6] Schneps L., “Dessins d'enfants on the Riemann Sphere”, The Grothendieck Theory of Dessins d'Enfants, LMS Lect. Notes, 200, Cambridge Univ. Press, Cambridge, 1994 | MR

[7] Lavrentev M.A., Shabat B.V., Metody teorii funktsii kompleksnogo peremennogo, Gos. izd-vo tekhn.-teor. lit-ry, M.–L., 1951 | MR