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Tr. Mat. Inst. Steklova, 2019, Volume 307, Pages 306–318 (Mi tm4039)  

Belyi Pairs and Fried Families

G. B. Shabat

Russian State University for the Humanities, Miusskaya pl. 6, Moscow, 125993 Russia

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.

Funding Agency Grant Number
Simons Foundation
The work was supported in part by the Simons Foundation.


DOI: https://doi.org/10.4213/tm4039

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English version:
Proceedings of the Steklov Institute of Mathematics, 2019, 307, 281–293

Bibliographic databases:

UDC: 511.6+512.72+512.77
Received: May 29, 2019
Revised: June 20, 2019
Accepted: September 1, 2019

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, Tr. 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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\paper Belyi Pairs and Fried Families
\inbook Algebra, number theory, and algebraic geometry
\bookinfo Collected papers. Dedicated to the memory of Academician Igor Rostislavovich Shafarevich
\serial Tr. Mat. Inst. Steklova
\yr 2019
\vol 307
\pages 306--318
\publ Steklov Mathematical Institute of RAS
\publaddr Moscow
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\pages 281--293
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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