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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2019, Volume 307, Pages 306–318
DOI: https://doi.org/10.4213/tm4039 (Mi tm4039) 		 
Belyi Pairs and Fried Families

G. B. Shabat

Russian State University for the Humanities, Miusskaya pl. 6, Moscow, 125993 Russia
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DOI: https://doi.org/10.4213/tm4039
Abstract: For the rational functions on algebraic curves, the number of critical values typical for the Belyi functions is three. This number is replaced by four. The emerging objects, unlike the rigid Belyi pairs, can be deformed; they constitute one-parameter families. The main properties of the corresponding curves in the moduli spaces are established, and the relation of these curves to the Belyi pairs is considered. The case of the clean Belyi pairs of genus $2$ of minimal degree $8$ is analyzed.
Keywords: Belyi pairs, dessins d'enfants, Fried families, moduli spaces of curves, Galois theory.
Funding agency Grant number
Simons Foundation
The work was supported in part by the Simons Foundation.
Received: May 29, 2019
Revised: June 20, 2019
Accepted: September 1, 2019
English version:
Proceedings of the Steklov Institute of Mathematics, 2019, Volume 307, Pages 281–293
DOI: https://doi.org/10.1134/S0081543819060178
Bibliographic databases:
Document Type: Article
UDC: 511.6+512.72+512.77
Language: Russian
Citation: G. B. Shabat, “Belyi Pairs and Fried Families”, Algebra, number theory, and algebraic geometry, Collected papers. Dedicated to the memory of Academician Igor Rostislavovich Shafarevich, Trudy Mat. Inst. Steklova, 307, Steklov Mathematical Institute of RAS, Moscow, 2019, 306–318; Proc. Steklov Inst. Math., 307 (2019), 281–293
Citation in format AMSBIB
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\pages 306--318
\publ Steklov Mathematical Institute of RAS
\publaddr Moscow
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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