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Full-Text Articles in Algebraic Geometry
Quasi-Platonic Psl2(Q)-Actions On Closed Riemann Surfaces, Sean A. Broughton
Quasi-Platonic Psl2(Q)-Actions On Closed Riemann Surfaces, Sean A. Broughton
S. Allen Broughton
This paper is the first of two papers whose combined goal is to explore the dessins d'enfant and symmetries of quasi-platonic actions of PSL2(q). A quasi-platonic action of a group G on a closed Riemann S surface is a conformal action for which S/G is a sphere and S->S/G is branched over {0, 1,infinity}. The unit interval in S/G may be lifted to a dessin d'enfant D, an embedded bipartite graph in S. The dessin forms the edges and vertices of a tiling on S by dihedrally symmetric polygons, generalizing the idea of a …