Acylindrical Actions for Two-Dimensional Artin Groups of Hyperbolic Type

For a two-dimensional Artin group A whose associated Coxeter group is hyperbolic, we prove that the action of A on the hyperbolic space obtained by coning off certain subcomplexes of its modified Deligne complex is acylindrical. Moreover, if for each s∈ S there is t∈ S with mₛₜ< ∞, then this action is universal. As a consequence, for |S|≥ 3, if A is irreducible, then it is acylindrically hyperbolic. We also obtain the Tits alternative for A, and we classify the subgroups of A that virtually split as a direct product. A key ingredient in our approach is a simple criterion to show the acylindricity of an action on a two-dimensional CAT(-1) complex.