FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2007, VOLUME 13, NUMBER 4, PAGES 95-112

Equations determining Belyi pairs, with applications to anti-Vandermonde systems

E. M. Kreines

Abstract

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This paper deals with Grothendieck dessins d'enfants, i.e., tamely embedded graphs on surfaces, and Belyi pairs, i.e., rational functions with at most three critical values on algebraic curves. The relationship between these objects was promoted by Grothendieck. We investigate combinatorics of systems of equations determining a Belyi pair corresponding to a given dessin. Some properties of extra, or so-called parasitic, solutions of such systems are described. As a corollary, we obtain some applications concerning anti-Vandermonde systems.

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Last modified: November 28, 2007