Almost Abelian regular dessins d%26apos;enfants

作者：Hidalgo Ruben A^*

来源：Fundamenta Mathematicae, 2013, 222(3): 269-278.

DOI：10.4064/fm222-3-3

• dessin d%26apos
• enfant
• Riemann surface
• algebraic curve
• field of definition
• field of moduli

A regular dessin d%26apos;enfant, in this paper, will be a pair (S, beta), where S is a closed Riemann surface and beta : S -%26gt; (C) over cap is a regular branched cover whose branch values are contained in the set {infinity, 0, 1}. Let Aut(S, beta) be the group of automorphisms of (S, beta), that is, the deck group of beta. If Aut(S, beta) is Abelian, then it is known that (S, beta) can be defined over Q. We prove that, if A is an Abelian group and Aut(S, beta) congruent to A (sic) Z(2), then (S, beta) is also definable over Q. Moreover, if A congruent to Z(n), then we provide explicitly these dessins over Q.

• 出版日期2013