Line arrangements modeling curves of high degree: equations, syzygies   and secants
  We study curves consisting of unions of projective lines whose intersections are given by graphs. Under suitable hypotheses on the graph, these so-called \emph{graph curves} can be embedded in projective space as line arrangements. We discuss property $N_p$ for these embeddings and are able to produce products of linear forms that generate the ideal in certain cases. We also briefly discuss questions regarding the higher-dimensional subspace arrangements obtained by taking the secant varieties of graph curves. 
Gregory Burnham, Zvi Rosen, Jessica Sidman, Peter Vermeire
math.AG math.AC math.CO