Combinatoire des arbres planaires et arithmétique des courbes hyperelliptiques. (Combinatorics of planar trees and arithmetics of hyperelliptic curves)

DOI10.5802/aif.1620zbMath0911.14013OpenAlexW2134407925MaRDI QIDQ1266216

Fedor Pakovitch

Publication date: 14 September 1998

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1998__48_2_323_0

zbMATH Keywords

hyperelliptic curvesGalois theorydessins d'enfantstreesBelyi functionstorsion points on elliptic curvesShabat polynomials

Mathematics Subject Classification ID

Galois theory (11R32) Arithmetic ground fields for curves (14H25) Enumerative problems (combinatorial problems) in algebraic geometry (14N10) Elliptic curves (14H52) Coverings of curves, fundamental group (14H30)

Related Items (9)

Betti maps, Pell equations in polynomials and almost-Belyi maps ⋮ On trees covering chains or stars ⋮ Geometric Properties of Inverse Polynomial Images ⋮ Abel pairs and modular curves ⋮ Calculating and drawing Belyi pairs ⋮ Rational functions with two critical points of maximum multiplicity ⋮ Description of inverse polynomial images which consist of two Jordan arc with the help of Jacobi's elliptic functions ⋮ True trees are dense ⋮ Pell-Abel equation and applications

Cites Work

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• Computation and rationality of Belyi functions in genus zero
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• Plane trees and Shabat polynomials
• Hill and toda curves
• ON GALOIS EXTENSIONS OF A MAXIMAL CYCLOTOMIC FIELD
• On some problems of the arithmetical theory of continued fractions II

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