Equations determining Belyi pairs,with applications to anti-Vandermonde systems |
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Authors: | E M Kreines |
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Institution: | (1) Moscow State University, Moscow, Russia |
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Abstract: | 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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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 4, pp. 95–112, 2007. |
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