Geodesic
On families of geometric parasitic solutions for Belyi systems of genus zero
Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 1, pp. 103-111.

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper is devoted to interrelations between the combinatorial structure of plane graphs and algebraic properties of systems of equations related to Belyi functions for these graphs. The main purpose is to describe some families of plane graphs possessing parasitic solutions and some families of plane graphs such that each solution of the corresponding systems is not parasitic and has multiplicity one. 
@article{FPM_2003_9_1_a8,
     author = {E. M. Kreines},
     title = {On families of geometric parasitic solutions for {Belyi} systems of genus zero},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {103--111},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2003_9_1_a8/}
}
TY  - JOUR
AU  - E. M. Kreines
TI  - On families of geometric parasitic solutions for Belyi systems of genus zero
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2003
SP  - 103
EP  - 111
VL  - 9
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2003_9_1_a8/
LA  - ru
ID  - FPM_2003_9_1_a8
ER  - 
%0 Journal Article
%A E. M. Kreines
%T On families of geometric parasitic solutions for Belyi systems of genus zero
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2003
%P 103-111
%V 9
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2003_9_1_a8/
%G ru
%F FPM_2003_9_1_a8
E. M. Kreines. On families of geometric parasitic solutions for Belyi systems of genus zero. Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 1, pp. 103-111. http://geodesic.mathdoc.fr/item/FPM_2003_9_1_a8/

[1] Adrianov N. M., Kochetkov Yu. Yu., Shabat G. B., Suvorov A. D., “Ploskie derevya i gruppy Mate”, Fundam. i prikl. mat., 1:2 (1995), 377–384 | MR | Zbl

[2] Belyi G. B., “O rasshireniyakh Galua maksimalnykh tsiklotomicheskikh polei”, Izv. AN SSSR, 43 (1979), 269–276 | MR

[3] Kreines E. M., Shabat G. B., “O paraziticheskikh resheniyakh sistem uravnenii na funktsii Belogo”, Fundam. i prikl. mat., 6:3 (2000), 789–792 | MR | Zbl

[4] Shafarevich I. R., Osnovy algebraicheskoi geometrii, Nauka, M., 1972 | MR | Zbl

[5] Bètrèma J., Pérè D., Zvonkine A., Plane trees and their Shabat polynomials, Catalog, Rapport Interne de LaBRI No 75–92, Bordeaux, 1992

[6] Grothendieck A., “Esquisse d'un programme”, London Math. Soc. Lecture Notes Series, 243, Cambridge Univ. Press, 1997, 3–43 | MR

[7] Kochetkov Yu. Yu., “Trees of diameter 4”, Proc. of the 12-th International Conference FPSAC-00, eds. Krob D., Mikhalev A. A., Mikhalev A. V., Springer, Berlin, 2000, 447–454 | MR

[8] Mulase M., Penkava M., Ribbon graphs, quadratic differentials on riemann surfaces, and algebraic curves defined over field of algebraic numbers, , November 1998 arXiv: /math-ph/9811024v2 | MR

[9] Shabat G., “On a class of families of Belyi functions”, Proc. of the 12-th International Conference FPSAC-00, eds. Krob D., Mikhalev A. A., Mikhalev A. V., Springer, Berlin, 2000, 575–581 | MR

[10] Shabat G. B., Voevodsky V. A., “Drowing curves over number fields”, The Grothendieck Festschrift, V. III, Birkhauser, 1990, 199–227 | MR | Zbl

[11] Shabat G., Zvonkine A., “Plane trees and algebraic numbers”, Contemporary Mathematics, 178 (1994), 233–275 | MR | Zbl