The bipartite graphs of abelian dessins d'enfants - Hidalgo, Rubén A. (Ars mathematica contemporanea, 2013)
Let ?$S$? be a closed Riemann surface and let ?$β \colon S → \widehat{\mathbb C}$? be a regular branched holomorphic covering, with an abelian group as deck group, whose branch values are contained in the set ?$\{ ∞, 0, 1 \}$?. Three dessins d'enfants are provided by ?$β^{- 1}(0, 1),\; β^{- 1}(1, ∞)$? and ?$β^{- 1}(0, ∞)$?. In this paper we provide a description of the bipartite graphs associated to these dessins d'enfants using simple arguments.
Keywords: algebraic curves; Belyi curves; dessins d'enfants; Riemann surfaces