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Real geometry of dessins d’enfant: a study of irreducible components. (Géométrie réelle des dessins d’enfant: une étude des composantes irréductibles.) (French) Zbl 1153.14308

Summary: The author continues her program started in [J. Théor. Nombres Bordx. 16, No. 3, 639–691 (2004; Zbl 1078.14089)] of using real algebraic geometry to study dessins d’enfant. In this paper, she studies the properties of the irreducible components associated with the real geometry of a dessin d’enfant. In other words, she gives a description of the irreducible components of the curve \(\Gamma \), the real points of which correspond to the preimage of the real projective line by a Belyi function of a dessin d’enfant.

MSC:

14P25 Topology of real algebraic varieties
14H30 Coverings of curves, fundamental group
14H57 Dessins d’enfants theory
11G32 Arithmetic aspects of dessins d’enfants, Belyĭ theory

Citations:

Zbl 1078.14089
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References:

[1] Ch. Birkenhake, H. Lange, Complex Abelian Varieties. Grundlehren der mathematischen Wissenchaften 302, A Series of Comprehensive Studies in Mathematics, Springer-Verlag, 1992. · Zbl 0779.14012
[2] L. Pharamond dit d’Costa, Géométrie réelle des dessins d’enfant. Journal de théorie des nombres de Bordeaux 16 (2004), 639-691. · Zbl 1078.14089
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