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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 446, Pages 182–220 (Mi znsl6289)  
This article is cited in 6 scientific papers (total in 6 papers)

Calculating and drawing Belyi pairs

G. Shabat

Russian State University for the Humanities, Miusskaya pl., 6, 125993, Moscow
Full-text PDF (796 kB) Citations (6)
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Abstract: The article contains a survey of the current state of the constructive part of the theory of dessin d'enfants. Namely, it is devoted to the actual establishing the correspondence between Belyi pairs and their combinatorial-topological representation. This correspondence is established in terms of the categorical equivalences, for which the necessary categories are introduced. Several connections with arithmetic are discussed. A section is devoted to one of the possible generalizations of the theory, in which the 3 branch points, allowed for the Belyi functions, are replaced by 4. Several direction of further research are presented.
Key words and phrases: dessins d'enfants, Belyi pairs, Riemann surfaces, absolute Galois group.
Received: 18.06.2016
English version:
Journal of Mathematical Sciences (New York), 2017, Volume 226, Issue 5, Pages 667–693
DOI: https://doi.org/10.1007/s10958-017-3557-3
Bibliographic databases:
Document Type: Article
UDC: 512.772.7
Language: English
Citation: G. Shabat, “Calculating and drawing Belyi pairs”, Combinatorics and graph theory. Part V, Zap. Nauchn. Sem. POMI, 446, POMI, St. Petersburg, 2016, 182–220; J. Math. Sci. (N. Y.), 226:5 (2017), 667–693
Citation in format AMSBIB
\Bibitem{Sha16}
\by G.~Shabat
\paper Calculating and drawing Belyi pairs
\inbook Combinatorics and graph theory. Part~V
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 446
\pages 182--220
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6289}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3520428}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 226
\issue 5
\pages 667--693
\crossref{https://doi.org/10.1007/s10958-017-3557-3}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85029680861}
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  • https://www.mathnet.ru/eng/znsl6289
  • https://www.mathnet.ru/eng/znsl/v446/p182
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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