Seminar Algebra and Geometry: Anne Lonjou (Basel)

Cremona group and hyperbolic spaces

The Cremona group is the group of birational transformations of the projective plane. It acts on a hyperbolic space which is an infinite dimensional version of the hyperboloid model of Hⁿ. This action is the main recent tool to study the Cremona group. After defining it, we will study its Voronoï tesselation, and describe some graphs naturally associated with this construction. Finally we will discuss which of these graphs are Gromov-hyperbolic.

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