Classical curves via one-vertex maps

Details Classical curves via one-vertex maps Classical curves via one-vertex maps

2012-01-08

arxiv.org/abs/1201.1646v2

Mathematics

Algebraic Geometry

16 pages, 4 figures, 2 tables

Scientific paper

One-vertex maps (a type of dessin d'enfant) give a uniform characterization of certain well-known algebraic curves, including those of Klein, Wiman, Accola-Maclachlan and Kulkarni. The characterization depends on a new classification of one-vertex (dually, one-face or unicellular) maps according to the size of the group of map automorphisms. We use an equivalence relation appropriate for studying the faithful action of the absolute Galois group on dessins, although we do not pursue that line of inquiry here.

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