Pavage de Voronoï associé au groupe de Cremona

Abstract

The action of the Cremona group of rank $2$ on an infinite dimensional hyperbolic space is the main recent tool to study the Cremona group. Following~the analogy with the action of $\operatorname{PSL}(2,\mathbb{Z})$ on the Poincaré half-plane, we exhibit a fundamental domain for this action by considering a Voronoi tessellation. Then we study adjacent cells to a given cell, as well as cells that share common points in the boundary at infinity.