Almost Abelian regular dessins d'enfants

Ruben A. Hidalgo. "Almost Abelian regular dessins d'enfants." Fundamenta Mathematicae 222.3 (2013): 269-278. <http://eudml.org/doc/286520>.

@article{RubenA2013,
abstract = {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.},
author = {Ruben A. Hidalgo},
journal = {Fundamenta Mathematicae},
keywords = {dessin d'enfant; Riemann surface; algebraic curve; field of definition; field of moduli},
language = {eng},
number = {3},
pages = {269-278},
title = {Almost Abelian regular dessins d'enfants},
url = {http://eudml.org/doc/286520},
volume = {222},
year = {2013},
}

TY - JOUR
AU - Ruben A. Hidalgo
TI - Almost Abelian regular dessins d'enfants
JO - Fundamenta Mathematicae
PY - 2013
VL - 222
IS - 3
SP - 269
EP - 278
AB - 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.
LA - eng
KW - dessin d'enfant; Riemann surface; algebraic curve; field of definition; field of moduli
UR - http://eudml.org/doc/286520
ER -