Pavage de Vorono\"i associ\'e au groupe de Cremona

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 PSL(2,Z) on the Poincar'e half-plane, we exhibit a fundamental domain for this action by considering a Vorono"i tessellation. Then we study adjacent cells to a given cell, as well as cells that share common points in the boundary at infinity.