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.

Location: http://mech.math.msu.su/~fpm/eng/k07/k074/k07405h.htm

Last modified: November 28, 2007