Almost Abelian regular dessins d'enfants

• Autorzy: Ruben A. Hidalgo
• Języki publikacji: EN

Abstrakty

EN

A regular dessin d'enfant, in this paper, will be a pair (S,β), where S is a closed Riemann surface and β: S → ℂ̂ is a regular branched cover whose branch values are contained in the set {∞,0,1}. Let Aut(S,β) be the group of automorphisms of (S,β), that is, the deck group of β. If Aut(S,β) is Abelian, then it is known that (S,β) can be defined over ℚ. We prove that, if A is an Abelian group and Aut(S,β) ≅ A ⋊ ℤ₂, then (S,β) is also definable over ℚ. Moreover, if A ≅ ℤₙ, then we provide explicitly these dessins over ℚ.

Kategorie tematyczne

• 30F10: Compact Riemann surfaces and uniformization
• 14H57: Dessins d'enfants theory
• 05C65: Hypergraphs

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2013
• Tom: 222
• Numer: 3
• Strony: 269-278

Daty

wydano

2013

Twórcy

autor

Ruben A. Hidalgo

• Departamento de Matemática, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaíso, Chile

Identyfikatory

DOI

10.4064/fm222-3-3