Sur l'hyperbolicit\'e de graphes associ\'es au groupe de Cremona
Group Theory
2023-06-22 v3 Algebraic Geometry
Abstract
To reinforce the analogy between the mapping class group and the Cremona group of rank over an algebraic closed field, we look for a graph analoguous to the curve graph and such that the Cremona group acts on it non-trivially. A candidate is a graph introduced by D. Wright. However, we demonstrate that it is not Gromov-hyperbolic. This answers a question of A. Minasyan and D. Osin. Then, we construct two graphs associated to a Vorono\"i tesselation of the Cremona group introduced in a previous work of the autor. We show that one is quasi-isometric to the Wright graph. We prove that the second one is Gromov-hyperbolic.
Cite
@article{arxiv.1802.02910,
title = {Sur l'hyperbolicit\'e de graphes associ\'es au groupe de Cremona},
author = {Anne Lonjou},
journal= {arXiv preprint arXiv:1802.02910},
year = {2023}
}
Comments
29 pages, en Fran\c{c}ais