Acylindrical hyperbolicity for Artin groups of dimension 2

Abstract

In this paper, we show that every irreducible $2$-dimensional Artin group $A_{\Gamma}$ of rank at least $3$ is acylindrically hyperbolic. We do this by studying the action of $A_{\Gamma}$ on its modified Deligne complex. Along the way, we prove results of independent interests on the geometry of links of this complex.