Federica Gavazzi

A Deligne Complex for Virtual Artin Groups

Virtual Artin groups, introduced by Bellingeri, Paris, and Thiel, are a generalisation of Artin groups containing embedded copies of both Artin and Coxeter groups. Many natural questions about Artin groups remain open and are often studied using geometric methods, in particular through actions on non-positively curved spaces. In this talk, we will consider an analogue of the Deligne complex for virtual Artin groups and show that it is CAT(0) for a certain subclass of defining graphs. As a consequence of this action, we classify the finite subgroups of locally reducible virtual Artin groups, showing that, up to conjugacy, they are contained in the corresponding copy of the Coxeter group.