Quasi-Projectivity of Weighted Right-Angled Artin Groups

Weighted right-angled Artin groups generalize right-angled Artin groups by adding weights to the edges of the defining graphs. We classify the weighted right-angled Artin groups that occur as fundamental groups of smooth complex quasi-projective varieties. They are precisely the finite direct products of finitely generated free groups and groups of the form $⟨a,b\mid [a,b{]}^m=1⟩$.