Acylindrical Actions for Two-Dimensional Artin Groups of Hyperbolic Type

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