Arrangements of hypersurfaces and Bestvina-Brady groups

TL;DR

This paper demonstrates that certain Bestvina-Brady groups can be realized as fundamental groups of hyperplane arrangement complements and explores their finiteness properties.

Contribution

It establishes a connection between quasi-projective Bestvina-Brady groups and hyperplane arrangement complements, expanding understanding of their topological and algebraic properties.

Findings

Bestvina-Brady groups are fundamental groups of hyperplane arrangement complements

Normal subgroups of right-angled Artin groups relate to hypersurface arrangements

Examples of hypersurface complements with specific finiteness properties

Abstract

We show that quasi-projective Bestvina-Brady groups are fundamental groups of complements to hyperplane arrangements. Furthermore we relate other normal subgroups of right-angled Artin groups to complements to arrangements of hypersurfaces. We thus obtain examples of hypersurface complements whose fundamental groups satisfy various finiteness properties.