Abstract: To any graph, one may associate three flavors of hyperplane arrangements: linear (subspaces of a complex vector space), toric (subtori of a complex torus), or abelian (abelian subvarieties of a complex abelian variety). In the linear case, there is considerable literature on the rational homotopy theory of the complement, and the toric case is similar in flavor. The abelian case is more complicated due to lack of formality of the space. When the graph is chordal, we have a Koszul model and use quadratic-linear duality to compute the minimal model and show that the space is rationally $K(\pi,1)$. This is joint work with Justin Hilburn.