Скачать или смотреть S. Lamy - Methods from geometric group theory 2.1

I shall discuss the action of the Cremona group on the infinite dimensional space of b-divisors (where b stands for birational), obtained as a limit of all Néron-Severi spaces for all possible blowups dominating the projective plane. This space is naturally endowed with a quadratic form of Minkowski type, and so contains an infinite dimensional hyperboloid. One application of this construction is to produce many normal subgroups in the Cremona group, via a general result in small cancellation theory. More generally, the action allows to classify elements or subgroups or the Cremona group along the familiar elliptic/parabolic/loxodromic subtypes in hyperbolic geometry. I plan to discuss a few classification results along these lines, for instance subgroups that contain a positive dimensional algebraic normal subgroup, or subgroups of elliptic elements that do not preserve a pencil of rational curves.

https://if-summer2025.sciencesconf.org